First Edition, 2012 ISBN 978-81-323-0832-4 © All rights reserved. Published by: Academic Studio 4735/22 Prakashdeep Bldg, Ansari Road, Darya Ganj, Delhi - 110002 Email: info@wtbooks.com 

Table of Contents

Chapter 1 - Introduction to Aerospace Engineering

Chapter 2 - Aviation History

Chapter 3 - Elements of Aerospace Engineering

Chapter 4 - Gravity Assist

Chapter 5 - Introduction to Aerodynamics

Chapter 6 - Lift (force) and Drag

Chapter 7 - Reynolds Number and Mach Number

Chapter 8 - Compressible Aerodynamics

Chapter 1

Introduction to Aerospace Engineering

Aerospace engineer

NASA engineers, like the ones depicted in Apollo 13, worked

diligently to protect the lives of the astronauts on the mission.

Occupation

Names engineer

aerospace engineer

Type profession

Activity sectors aeronautics, astronautics, science

Description

Competencies technical knowledge, management

skills

Fields of employment technology, science, military

Aerospace engineering is the branch of engineering behind the design, construction and science of aircraft and spacecraft. It is broken into two major and overlapping branches: aeronautical engineering and astronautical engineering. The former deals with craft that stay within Earth's atmosphere, and the latter deals with craft that operate outside of Earth's atmosphere.

While aeronautical engineering was the original term, the broader "aerospace" has superseded it in usage, as flight technology advanced to include craft operating in outer space. Aerospace engineering, particularly the astronautics branch, is often informally called rocket science.

Overview Flight vehicles undergo severe conditions such as differences in atmospheric pressure, and temperature, with structural loads applied upon vehicle components. Consequently, they are usually the products of various technological and engineering disciplines including aerodynamics, avionics, materials science and propulsion, structural analysis and Manufacturing. These technologies are collectively known as aerospace engineering. Because of the complexity of the field, aerospace engineering is conducted by a team of engineers, each specializing in their own branches of science.

The development and manufacturing of a modern flight vehicle is an extremely complex process and demands careful balance and compromise between abilities, design, available technology and costs. Aerospace engineers design, test, and supervise the manufacture of aircraft, spacecraft, and missiles. Aerospace engineers develop new technologies for use in aviation, defense systems, and space exploration.

Aerospace engineering degrees

Aerospace engineering

Aerospace engineering can be studied at the advanced diploma, bachelor's, master's, and Ph.D. levels in aerospace engineering departments at many universities, and in mechanical engineering departments at others. A few departments offer degrees in space-focused astronautical engineering. The Delft University of Technology (TU Delft) in the Netherlands offers one of the top European aerospace educational and research platforms, while the programs of the Massachusetts Institute of Technology and Rutgers University are two such examples. In 2009, U.S. News & World Report ranked the undergraduate aerospace engineering programs at the Massachusetts Institute of Technology, Georgia Institute of Technology, and the University of Michigan as the top three best programs for doctorate granting universities in the United States. The other programs in the top ten were Purdue University, California Institute of Technology, University of Maryland, University of Illinois, Stanford University, University of Texas at Austin, and Virginia Tech in that order. The magazine also rates Embry-Riddle Aeronautical University, the United States Air Force Academy, and the United States Naval Academy as the premier aerospace engineering programs at universities that do not grant doctorate degrees. Wichita State University is renowned for its Aerospace Engineering program and also has the third highest research budget for Aerospace Engineering in the United States.

In Canada, the University of Toronto has a quality aerospace engineering program. The aerospace program requires the students to go through a competitive program called engineering science. The academic program in aerospace science and engineering at U of T includes undergraduate and graduate studies. At the graduate level U of T offers research-intensive programs leading to MASc and PhD degrees, and a professionally-

oriented program leading to the MEng degree. The scope of U of T's research includes aeronautical engineering (aircraft flight systems, propulsion, aerodynamics, computational fluid dynamics, and structural mechanics) and space systems engineering (spacecraft dynamics and control, space robotics and mechatronics, and microsatellite technology). Carleton University and Ryerson University are other top aerospace engineering universities in Canada which offer accredited graduate and under-graduate degrees.

In the UK, Aerospace (or aeronautical) engineering can be studied for the B.Eng., M.Eng., MSc. and Ph.D. levels at a number of universities. The top 10 universities are University of Cambridge, University of Surrey, University of Bristol, University of Southampton, Queens University Belfast, University of Sheffield, Newcastle University, University of Bath, Imperial College London, Loughborough University and University of Nottingham for 2010. The Department of Aeronautics at Imperial College London is noted for providing engineers for the Formula One industry, an industry that uses aerospace technology.

Aerospace can be studied at University of Limerick in Ireland. In Australia, the RMIT University offers Aerospace (or aeronautical) engineering and has more than 60 years teaching experience in this profession. Monash University, University of New South Wales, University of Sydney, University of Queensland, University of Adelaide and Queensland University of Technology also offers Aerospace Engineering.

European universities that are renowned for their teaching and expertise in aerospace engineering include TU Delft in the Netherlands, and ENAC in France, RWTH Aachen, TU München, the University of Stuttgart, TU Berlin and TU Braunschweig in Germany. In Austria the FH Joanneum. In Spain the Universidad Politecnica de Madrid, the Universidad Carlos III de Madrid, and Universitat Politècnica de Catalunya offer the degree, while in Italy there also several universities where aerospace engineering can be studied including the Politecnico di Torino, the University of Pisa and the Politecnico di Milano. In Eastern Europe they are the University of Belgrade, the Warsaw University of Technology and Rzeszów University of Technology in Poland and Brno University of Technology in Brno, Czech Republic.

In India IIT Kanpur possesses its own flight test aircraft and airfield for students in the discipline, while the other IITs also offer degrees in this discipline. From academic year 2010 onwards Bengal Engineering and Science University, Shibpur has started offering an undergraduate course Bachelor of Engineering in Aerospace Engineering. While in China Nanjing Aeronautics and Astronautics University is a regional leader in the field of aerospace engineering education. In Pakistan Aerospace Engineering can be studied at National University of Sciences and Technology at (CAE), at PAF Academy in Risalpur & at Air University which is Pakistan's only university that grants a Doctorate degree in Aerospace Engineering & Avionics Engineering. In 2002, SUPARCO established IST which is a federally chartered public sector institute of Pakistan offering under graduate and graduate degree in Aerospace Engineering. The MS degree at IST is being offered in

collaboration with Beihang University (BUAA), China and Seoul National University, South Korea

Chapter 2

Aviation History

Aviation History

French reconnaissance balloon L'Intrépide of 1796, the oldest existing flying device, in the Heeresgeschichtliches Museum,

Vienna

Leonardo da Vinci's "aerial screw" design.

Leonardo da Vinci's Ornithopter design.

Aviation history refers to the history of development of mechanical flight—from the earliest attempts in kites and gliders to powered heavier-than-air, supersonic and spaceflights.

The first form of man-made flying objects were kites. The earliest known record of kite flying is from around 200 B.C. in China, when a General flew a kite over enemy territory to calculate the length of tunnel required to enter the region. Yuan Huangtou, a Chinese prince, survived by tying himself to the kite.

Leonardo da Vinci's (15th c.) dream of flight found expression in several designs, but he did not attempt to demonstrate flight by literally constructing them.

With the efforts to analyze the atmosphere in the 17th and 18th century, gases such as hydrogen were discovered which in turn led to the invention of hydrogen balloons. Various theories in mechanics by physicists during the same period of time—notably fluid dynamics and Newton's laws of motion—led to the foundation of modern aerodynamics. Tethered balloons filled with hot air were used in the first half of the 19th century and saw considerable action in several mid-century wars, most notably the American Civil War, where balloons provided observation during the Battle of Petersburg.

Experiments with gliders laid a groundwork to build heavier-than-air craft, and by the early 20th century advancements in engine technology and aerodynamics made controlled, powered flight possible for the first time.

Mythology

Daedalus working on Icarus' wings. Illustration from a relief in Villa Albani, Rome, 1st-2nd century CE.

Human ambition to fly is illustrated in mythological literature of several cultures; the wings made out of wax and feathers by Daedalus in Greek mythology, or the Pushpaka Vimana of king Ravana in Ramayana, for instance.

Early attempts

Flight automaton in Greece

Around 400 B.C., Archytas, the Greek philosopher, mathematician, astronomer, statesman and strategist, designed and built a bird-shaped, apparently steam powered model named "The Pigeon" (Greek: Περιστέρα "Peristera"), which is said to have flown some 200 meters. According to Aulus Gellius, the mechanical bird was suspended on a string or pivot and was powered by a "concealed aura or spirit".

Hot air balloons and kites in China

The Kongming lantern (proto hot air balloon) was known in China from ancient times. Its invention is usually attributed to the general Zhuge Liang (180–234 AD, honorific title Kongming), who is said to have used them to scare the enemy troops:

An oil lamp was installed under a large paper bag, and the bag floated in the air due to the lamp heating the air. ... The enemy was frightened by the light in the air, thinking that some divine force was helping him.

However, the device based on a lamp in a paper shell is documented earlier, and according to Joseph Needham, hot-air balloons in China were known from the 3rd century BC.

In the 5th century BCE Lu Ban invented a 'wooden bird' which may have been a large kite, or which may have been an early glider.

During the Yuan dynasty (13th c.) under rulers like Kublai Khan, the rectangular lamps became popular in festivals, when they would attract huge crowds. During the Mongol Empire, the design may have spread along the Silk Route into Central Asia and the Middle East. Almost identical floating lights with a rectangular lamp in thin paper scaffolding are common in Tibetan celebrations and in the Indian festival of lights, Diwali. However, there is no evidence that these were used for human flight.

Gliders in Europe

Stained glass window showing Eilmer, installed in Malmesbury Abbey in 1920

In the 9th century, at the age of 65, the Berber polymath Ibn Firnas is said to have flown from the hill Jabal al-'arus by employing a rudimentary glider. While "alighting again on the place whence he had started," he eventually crashed and sustained injury which some contemporary critics attributed to a lack of tail. However, the only source describing the event is from the 17th century.

Between 1000 and 1010, the English Benedictine monk Eilmer of Malmesbury flew for about 200 meters using a glider (circa 1010), but sustained injuries, too. The event is recorded in the work of the eminent medieval historian William of Malmesbury in about

1125. Being a fellow monk in the same abbey, William almost certainly obtained his account directly from people there who knew Eilmer himself.

From Renaissance to the 18th century

Leonardo da Vinci's Ornithopter wings

Some six centuries after Ibn Firnas, Leonardo da Vinci developed a hang glider design in which the inner parts of the wings are fixed, and some control surfaces are provided towards the tips (as in the gliding flight in birds). While his drawings exist and are deemed flightworthy in principle, he himself never flew in it. Based on his drawings, and using materials that would have been available to him, a prototype constructed in the late 20th century was shown to fly. However, his sketchy design was interpreted with modern knowledge of aerodynamic principles, and whether his actual ideas would have flown is not known. A model he built for a test flight in 1496 did not fly, and some other designs, such as the four-person screw-type helicopter have severe flaws.

In 1670 Francesco Lana de Terzi published work that suggested lighter than air flight would be possible by having copper foil spheres that contained a vacuum that would be lighter than the displaced air, lift an airship (rather literal from his drawing). While not being completely off the mark, he did fail to realize that the pressure of the surrounding air would smash the spheres.

The small Priekule Lutheran Church in Latvia is related to an old legend about Ikarus of Priekule. For almost two centuries time after time in various printed texts- periodicals and books- there is described a sensational event that happened in the second half of the 17th century (according to another version at the beginning of the 18th century). People of Priekule have been telling their children this legend for many centuries. The blacksmith of Priekule Zviedris (Swede) Johanson (by nationality Swede?) made wings and from the steeple of the church made his first flight. Later the flight was announced as an unforgivable blasphemy. The local Ikarus was announced the Satan’s avatar and was burned alive at the stake.

In 1709, Bartolomeu de Gusmão presented a petition to King John V of Portugal, begging a privilege for his invention of an airship, in which he expressed the greatest confidence. The public test of the machine, which was set for June 24, 1709, did not take place. According to contemporary reports, however, Gusmão appears to have made several less ambitious experiments with this machine, descending from eminences. It is certain that Gusmão was working on this principle at the public exhibition he gave before the Court on August 8, 1709, in the hall of the Casa da Índia in Lisbon, when he propelled a ball to the roof by combustion.

Modern flight

Lighter than air

The 1884 La France, the first fully controllable airship

Although many people think of human flight as beginning with the aircraft in the early 20th century, in fact people had been flying repeatedly for more than 100 years.

The first generally recognized human flight took place in Paris in 1783. Jean-François Pilâtre de Rozier and François Laurent d'Arlandes went 8 km (5 miles) in a hot air balloon invented by the Montgolfier brothers. The balloon was powered by a wood fire, and was not steerable: that is, it flew wherever the wind took it.

The navigable balloon created by Giffard in 1852

Ballooning became a major "rage" in Europe in the late 18th century, providing the first detailed understanding of the relationship between altitude and the atmosphere.

Work on developing a steerable (or dirigible) balloon (now called an airship) continued sporadically throughout the 19th century. The first powered, controlled, sustained lighter-than-air flight is believed to have taken place in 1852 when Henri Giffard flew 15 miles (24 km) in France, with a steam engine driven craft.

Non-steerable balloons were employed during the American Civil War by the Union Army Balloon Corps.

Another advance was made in 1884, when the first fully controllable free-flight was made in a French Army electric-powered airship, La France, by Charles Renard and Arthur Krebs. The 170-foot (52 m) long, 66,000-cubic-foot (1,900 m3) airship covered 8 km (5 miles) in 23 minutes with the aid of an 8½ horsepower electric motor.

However, these aircraft were generally short-lived and extremely frail. Routine, controlled flights would not come to pass until the advent of the internal combustion engine (see below.)

Although airships were used in both World War I and II, and continue on a limited basis to this day, their development has been largely overshadowed by heavier-than-air craft.

Heavier-than-air

Sustaining the aircraft

Sir George Cayley's governable parachute

The first published paper on aviation was "Sketch of a Machine for Flying in the Air" by Emanuel Swedenborg published in 1716. This flying machine consisted of a light frame covered with strong canvas and provided with two large oars or wings moving on a horizontal axis, arranged so that the upstroke met with no resistance while the downstroke provided lifting power. Swedenborg knew that the machine would not fly, but suggested it as a start and was confident that the problem would be solved. He said, "It seems easier to talk of such a machine than to put it into actuality, for it requires greater force and less weight than exists in a human body. The science of mechanics might perhaps suggest a means, namely, a strong spiral spring. If these advantages and requisites are observed, perhaps in time to come some one might know how better to utilize our sketch and cause some addition to be made so as to accomplish that which we can only suggest. Yet there are sufficient proofs and examples from nature that such flights can take place without danger, although when the first trials are made you may

have to pay for the experience, and not mind an arm or leg." Swedenborg would prove prescient in his observation that powering the aircraft through the air was the crux of flying.

During the last years of the 18th century, Sir George Cayley started the first rigorous study of the physics of flight. In 1799 he exhibited a plan for a glider, which except for planform was completely modern in having a separate tail for control and having the pilot suspended below the center of gravity to provide stability, and flew it as a model in 1804. Over the next five decades Cayley worked on and off on the problem, during which he invented most of basic aerodynamics and introduced such terms as lift and drag. He used both internal and external combustion engines, fueled by gunpowder. Later Cayley turned his research to building a full-scale version of his design, first flying it unmanned in 1849, and in 1853 his coachman made a short flight at Brompton, near Scarborough in Yorkshire.

In 1848, John Stringfellow had a successful indoor test flight of a steam-powered model, in Chard, Somerset, England.

Model of Jan Wnęk's glider. Kraków Museum of Ethnography.

In 1866 a Polish peasant, sculptor and carpenter by the name of Jan Wnęk built and flew a controllable glider. Wnęk was illiterate and self-taught, and could only count on his knowledge about nature based on observation of birds' flight and on his own builder and carver skills. Jan Wnęk was firmly strapped to his glider by the chest and hips and controlled his glider by twisting the wing's trailing edge via strings attached to stirrups at his feet. Church records indicate that Jan Wnęk launched from a special ramp on top of the Odporyszów church tower; The tower stood 45 m high and was located on top of a 50 m hill, making a 95 m (311 ft) high launch above the valley below. Jan Wnęk made several public flights of substantial distances between 1866 and 1869, especially during religious festivals, carnivals and New Year celebrations. Wnęk left no known written records or drawings, thus having no impact on aviation progress. Recently, Professor

Tadeusz Seweryn, director of the Kraków Museum of Ethnography, has unearthed church records with descriptions of Jan Wnęk's activities.

Jean-Marie Le Bris and his flying machine, Albatros II, 1868.

In 1856, Frenchman Jean-Marie Le Bris made the first flight higher than his point of departure, by having his glider "L'Albatros artificiel" pulled by a horse on a beach. He reportedly achieved a height of 100 meters, over a distance of 200 meters.

Francis Herbert Wenham built a series of unsuccessful unmanned gliders. He found that the most of the lift from a bird-like wing appeared to be generated at the front edge, and concluded correctly that long, thin wings would be better than the bat-like ones suggested by many, because they would have more leading edge for their weight. Today this measure is known as aspect ratio. He presented a paper on his work to the newly formed Aeronautical Society of Great Britain in 1866, and decided to prove it by building the world's first wind tunnel in 1871. Members of the Society used the tunnel and learned that cambered wings generated considerably more lift than expected by Cayley's Newtonian reasoning, with lift-to-drag ratios of about 5:1 at 15 degrees. This clearly demonstrated the ability to build practical heavier-than-air flying machines; what remained was the problem of controlling the flight and powering them.

Around 1871 Alphonse Pénaud made rubber powered model aircraft. While of little direct practical use they inspired a whole generation of future flight pioneers, including the Wright brothers who were given them as toys as children.

In 1874, Félix du Temple built the "Monoplane", a large plane made of aluminium in Brest, France, with a wingspan of 13 meters and a weight of only 80 kilograms (without the driver). Several trials were made with the plane, and it is generally recognized that it achieved lift off under its own power after a ski-jump run, glided for a short time and returned safely to the ground, making it the first successful powered flight in history, although the flight was only a short distance and a short time.

Félix du Temple's 1874 Monoplane.

Controlling the flight

The 1880s became a period of intense study, characterized by the "gentleman scientists" who represented most research efforts until the 20th century. Starting in the 1880s advancements were made in construction that led to the first truly practical gliders. Three people in particular were active: Otto Lilienthal, Percy Pilcher and Octave Chanute. One of the first truly modern gliders appears to have been built by John J. Montgomery; it flew in a controlled manner outside of San Diego on August 28, 1883. It was not until many years later that his efforts became well known. Another delta hang-glider had been constructed by Wilhelm Kress as early as 1877 near Vienna.

Otto Lilienthal of Germany duplicated Wenham's work and greatly expanded on it in 1874, publishing his research in 1889. He also produced a series of ever-better gliders, and in 1891 was able to make flights of 25 meters or more routinely. He rigorously documented his work, including photographs, and for this reason is one of the best known of the early pioneers. He also promoted the idea of "jumping before you fly", suggesting that researchers should start with gliders and work their way up, instead of simply designing a powered machine on paper and hoping it would work. His type of aircraft is now known as a hang glider.

By the time of his death in 1896 he had made 2500 flights on a number of designs, when a gust of wind broke the wing of his latest design, causing him to fall from a height of roughly 56 feet (17 m), fracturing his spine. He died the next day, with his last words being "small sacrifices must be made". Lilienthal had been working on small engines suitable for powering his designs at the time of his death.

Australian Lawrence Hargrave invented the box kite and dedicated his life to constructing flying machines. In the 1880s he experimented with monoplane models and by 1889 Hargrave had constructed a rotary airplane engine, driven by compressed air.

Picking up where Lilienthal left off, Octave Chanute took up aircraft design after an early retirement, and funded the development of several gliders. In the summer of 1896 his troop flew several of their designs many times at Miller Beach, Indiana, eventually deciding that the best was a biplane design that looks surprisingly modern. Like Lilienthal, he heavily documented his work while photographing it, and was busy corresponding with like-minded hobbyists around the world. Chanute was particularly interested in solving the problem of aerodynamic instability of the aircraft in flight, one which birds corrected for by instant corrections, but one that humans would have to address with stabilizing and control surfaces (or moving center of gravity, as Lilienthal did). The most disconcerting problem was longitudinal instability (divergence), because as the angle of attack of a wing increased, the center of pressure moved forward and made the angle increase more. Without immediate correction, the craft would pitch up and stall. Much more difficult to understand was the mixing of lateral/directional stability and control.

Powering the aircraft

Patent drawings of Clément Ader Eole

Clément Ader Avion III (1897 photograph).

Throughout this period, a number of attempts were made to produce a true powered aircraft. However the majority of these efforts were doomed to failure, being designed by hobbyists who did not have a full understanding of the problems being discussed by Lilienthal and Chanute.

In France Clément Ader built the steam-powered Eole and may have made a 50-meter flight near Paris in 1890, which would be the first self-propelled "long distance" flight in history. Ader then worked on a larger design which took five years to build. In a test for

the French military, the Avion III reportedly managed to cover 300 meters at a very small height, crashing out of control.

In 1884, Alexander Mozhaysky's monoplane design made what is now considered to be a power assisted take off or 'hop' of 60–100 feet (20–30 meters) near Krasnoye Selo, Russia.

Sir Hiram Maxim studied a series of designs in England, eventually building a monstrous 7,000 pounds (3,200 kg) design with a wingspan of 105 feet (32 m), powered by two advanced low-weight steam engines which delivered 180 hp (134 kW) each. Maxim built it to study the basic problems of construction and power and it remained without controls, and, realizing that it would be unsafe to fly, he instead had a 1,800 feet (550 m) track constructed for test runs. After a number of test runs working out problems, on July 31, 1894 they started a series of runs at increasing power settings. The first two were successful, with the craft "flying" on the rails. In the afternoon the crew of three fired the boilers to full power, and after reaching over 42 mph (68 km/h) about 600 feet (180 m) down the track the machine produced so much lift it pulled itself free of the track and crashed after flying at low altitudes for about 200 feet (61 m). Declining fortunes left him unable to continue his work until the 20th century, when he was able to test a number of smaller designs powered by gasoline.

In the United Kingdom an attempt at heavier-than-air flight was made by the aviation pioneer Percy Pilcher. Pilcher had built several working gliders, The Bat, The Beetle, The Gull and The Hawk, which he flew successfully during the mid to late 1890s. In 1899 he constructed a prototype powered aircraft which, recent research has shown, would have been capable of flight. However, he died in a glider accident before he was able to test it, and his plans were forgotten for many years.

The "Pioneer Era" (1900–1914)

Lighter than air

Santos-Dumont's "Number 6" rounding the Eiffel Tower in the process of winning the Deutsch Prize. Photo courtesy of the Smithsonian Institution (SI Neg. No. 85-3941)

The first aircraft to make routine controlled flights were non-rigid airships (later called "blimps".) The most successful early pioneering pilot of this type of aircraft was the Brazilian Alberto Santos-Dumont who effectively combined a balloon with an internal combustion engine. On October 19, 1901 he flew his airship "Number 6" over Paris from the Parc Saint Cloud around the Eiffel Tower and back in under 30 minutes to win the Deutsch de la Meurthe prize. Santos-Dumont went on to design and build several aircraft.

Subsequent controversy surrounding his and others' competing claims with regard to aircraft overshadowed his unparalleled contributions to the development of airships.

At the same time that non-rigid airships were starting to have some success, rigid airships were also becoming more advanced. Indeed, rigid body dirigibles would be far more capable than fixed wing aircraft in terms of pure cargo carrying capacity for decades. Dirigible design and advancement was brought about by the German count, Ferdinand von Zeppelin.

Construction of the first Zeppelin airship began in 1899 in a floating assembly hall on Lake Constance in the Bay of Manzell, Friedrichshafen. This was intended to ease the starting procedure, as the hall could easily be aligned with the wind. The prototype airship LZ 1 (LZ for "Luftschiff Zeppelin") had a length of 128 m, was driven by two 14.2 ps (10.6 kW) Daimler engines and balanced by moving a weight between its two nacelles.

The first Zeppelin flight occurred on July 2, 1900. It lasted for only 18 minutes, as LZ 1 was forced to land on the lake after the winding mechanism for the balancing weight had broken. Upon repair, the technology proved its potential in subsequent flights, beating the 6 m/s velocity record of French airship La France by 3 m/s, but could not yet convince possible investors. It would be several years before the Count was able to raise enough funds for another try. Indeed, it was not until 1902 when Spanish engineer Leonardo Torres Quevedo developed his own zeppelin airship, with which he solved the serious balance problems the suspending gondola had shown in previous flight attempts.

Heavier than air

Langley

First failure of Langley's manned Aerodrome on the Potomac River, October 7, 1903

After a distinguished career in astronomy and shortly before becoming Secretary of the Smithsonian Institution, Samuel Pierpont Langley started a serious investigation into aerodynamics at what is today the University of Pittsburgh. In 1891 he published

Experiments in Aerodynamics detailing his research, and then turned to building his designs. On May 6, 1896, Langley's Aerodrome No.5 made the first successful sustained flight of an unpiloted, engine-driven heavier-than-air craft of substantial size. It was launched from a spring-actuated catapult mounted on top of a houseboat on the Potomac River near Quantico, Virginia. Two flights were made that afternoon, one of 1,005 metres (3,297 ft) and a second of 700 metres (2,300 ft), at a speed of approximately 25 miles per hour (40 km/h). On both occasions the Aerodrome No.5 landed in the water as planned, because in order to save weight, it was not equipped with landing gear. On November 28, 1896, another successful flight was made with the Aerodrome No.6. This flight, of 1,460 metres (4,790 ft), was witnessed and photographed by Alexander Graham Bell. The Aerodrome No.6 was actually Aerodrome No.4 greatly modified. So little remained of the original aircraft that it was given the new designation of Aerodrome No.6.

With the success of the Aerodrome No. 5 and its follow-on No. 6, Langley started looking for funding to build a full-scale man-carrying version of his designs. Spurred by the Spanish-American War, the U.S. government granted him $50,000 to develop a man-carrying flying machine for surveillance. Langley planned on building a scaled-up version known as the Aerodrome A, and started with the smaller Quarter-scale Aerodrome, which flew twice on June 18, 1901, and then again with a newer and more powerful engine in 1903.

With the basic design apparently successfully tested, he then turned to the problem of a suitable engine. He contracted Stephen Balzer to build one, but was disappointed when it delivered only 8 horsepower (6 kW) instead of 12 hp (9 kW) as he expected. Langley's assistant, Charles M. Manly, then reworked the design into a five-cylinder water-cooled radial that delivered 52 horsepower (39 kW) at 950 rpm, a feat that took years to duplicate. Now with both power and a design, Langley put the two together with great hopes.

To his dismay, the resulting aircraft proved to be too fragile. He had apparently overlooked the effects of minimum gauge, and simply scaling up the original small models resulted in a design that was too weak to hold itself together. Two launches in late 1903 both ended with the Aerodrome immediately crashing into the water. The pilot, Manly, was rescued each time.

Langley's attempts to gain further funding failed, and his efforts ended. Nine days after his second abortive launch on December 8, the Wright brothers successfully flew their aptly-named Flyer. Glenn Curtiss made several modifications to the Aerodrome and successfully flew it in 1914—the Smithsonian Institution thus continued to assert that Langley's Aerodrome was the first machine "capable of flight".

The Wright Brothers

Following a step by step method, discovering aerodynamic forces then controlling the flight, the brothers built and tested a series of kite and glider designs from 1900 to 1902 before attempting to build a powered design. The gliders worked, but not as well as the

Wrights had expected based on the experiments and writings of their 19th century predecessors. Their first glider, launched in 1900, had only about half the lift they anticipated. Their second glider, built the following year, performed even more poorly. Rather than giving up, the Wrights constructed their own wind tunnel and created a number of sophisticated devices to measure lift and drag on the 200 wing designs they tested. As a result, the Wrights corrected earlier mistakes in calculations regarding drag and lift. Their testing and calculating produced a third glider with a larger aspect ratio and true three-axis control. They flew it successfully hundreds of times in 1902, and it performed far better than the previous models. In the end, by establishing their rigorous system of designing, wind-tunnel testing of airfoils and flight testing of full-size prototypes, the Wrights not only built a working aircraft but also helped advance the science of aeronautical engineering.

The Wright Flyer: the first sustained flight with a powered, controlled aircraft.

The Wrights appear to be the first design team to make serious studied attempts to simultaneously solve the power and control problems. Both problems proved difficult, but they never lost interest. They solved the control problem by inventing wing warping for roll control, combined with simultaneous yaw control with a steerable rear rudder. Almost as an afterthought, they designed and built a low-powered internal combustion engine. Relying on their wind tunnel data, they also designed and carved wooden propellers that were more efficient than any before, enabling them to gain adequate performance from their marginal engine power. Although wing-warping was used only briefly during the history of aviation, when used with a rudder it proved to be a key advance in order to control an aircraft. While many aviation pioneers appeared to leave

safety largely to chance, the Wrights' design was greatly influenced by the need to teach themselves to fly without unreasonable risk to life and limb, by surviving crashes. This emphasis, as well as marginal engine power, was the reason for low flying speed and for taking off in a head wind. Performance (rather than safety) was also the reason for the rear-heavy design, because the canard could not be highly loaded; anhedral wings were less affected by crosswinds and were consistent with the low yaw stability.

According to the Smithsonian Institution and Fédération Aéronautique Internationale (FAI), the Wrights made the first sustained, controlled, powered heavier-than-air manned flight at Kill Devil Hills, North Carolina, four miles (8 km) south of Kitty Hawk, North Carolina on December 17, 1903.

The first flight by Orville Wright, of 120 feet (37 m) in 12 seconds, was recorded in a famous photograph. In the fourth flight of the same day, Wilbur Wright flew 852 feet (260 m) in 59 seconds. The flights were witnessed by three coastal lifesaving crewmen, a local businessman, and a boy from the village, making these the first public flights and the first well-documented ones.

Orville described the final flight of the day: "The first few hundred feet were up and down, as before, but by the time three hundred feet had been covered, the machine was under much better control. The course for the next four or five hundred feet had but little undulation. However, when out about eight hundred feet the machine began pitching again, and, in one of its darts downward, struck the ground. The distance over the ground was measured to be 852 feet (260 m); the time of the flight was 59 seconds. The frame supporting the front rudder was badly broken, but the main part of the machine was not injured at all. We estimated that the machine could be put in condition for flight again in about a day or two." They flew only about ten feet above the ground as a safety precaution, so they had little room to maneuver, and all four flights in the gusty winds ended in a bumpy and unintended "landing". Modern analysis by Professor Fred E. C. Culick and Henry R. Rex (1985) has demonstrated that the 1903 Wright Flyer was so unstable as to be almost unmanageable by anyone but the Wrights, who had trained themselves in the 1902 glider.

The Wrights continued flying at Huffman Prairie near Dayton, Ohio in 1904–05. After a severe crash on 14 July 1905, they rebuilt the Flyer and made important design changes. They almost doubled the size of the elevator and rudder and moved them about twice the distance from the wings. They added two fixed vertical vanes (called "blinkers") between the elevators, and gave the wings a very slight dihedral. They disconnected the rudder from the wing-warping control, and as in all future aircraft, placed it on a separate control handle. When flights resumed the results were immediate. The serious pitch instability that hampered Flyers I and II was significantly reduced, so repeated minor crashes were eliminated. Flights with the redesigned Flyer III started lasting over 10 minutes, then 20, then 30. Flyer III became the first practical aircraft (though without wheels and needing a launching device), flying consistently under full control and bringing its pilot back to the starting point safely and landing without damage. On 5 October 1905, Wilbur flew 24 miles (39 km) in 39 minutes 23 seconds."

According to the April 1907 issue of the Scientific American magazine, the Wright brothers seemed to have the most advanced knowledge of heavier-than-air navigation at the time. Though, the same magazine issue also affirms that no public flight has been made in the United States before its April 1907 issue. Hence, they devised the Scientific American Aeronautic Trophy in order to encourage the development of a heavier-than-air flying machine.

Alberto Santos-Dumont

Alberto Santos-Dumont, the designer of the 14-bis.

The Brazilian inventor Alberto Santos-Dumont made a public flight with the flying machine designated 14-bis on 13 September 1906 in Paris. He used a canard elevator and pronounced wing dihedral, and covered a distance of 60 m (200 ft). Since the plane did not need headwinds or catapults to take off, this flight is considered by some as the first true powered flight. Also, since the earlier attempts of Pearse, Jatho, Watson, and the Wright brothers received far less attention from the popular press, Santos-Dumont's flight was more important to society when it happened, especially in Europe and Brazil, despite occurring some years later.

Confusion occasionally still arises over whether the Wright 1903 Flyer I, or the 14-Bis was the first true airplane. In fact, only the Wright Flyer I and its successors met the modern definition of an airplane (i.e., manned, powered, heavier than air, fully controllable around all three axes, and capable of sustained flight). The Wright 1903 Flyer I met this definition on December 17, 1903, taking off under its own power along a level wooden guide rail.

While the Wrights later used a launch catapult for their 1904 and 1905 machines, those Flyers could also take off unassisted given sufficient wind. It should be noted that the Wright 1905 Flyer (also called the Flyer III) flew more than 20 miles (32 km) in October 1905, a full year before the 14-bis made its first flight.

The 14-bis was marginally controllable at best and could only make wallowing hops. This remained true after Santos-Dumont, who was on the right track, installed primitive ailerons in November 1906. Unfortunately, they proved ineffective. On the plus side, Santos-Dumont and other Europeans used wheels whereas the Wrights stuck with skids for too long, which necessitated the use of a catapult in the absence of significant wind.

Santos-Dumont fans usually infer that while the Wright Flyer may have been superior in the air, its take-off apparatus made it overly impractical to operate and transport. Alternatively, Wright brothers fans usually point to the implication that the scarcity of usable takeoff fields made the Flyer and "pillar" more practical, needing much less open, smooth and level space than the 14-bis.

The 14-bis also known as Oiseau de proie (French for "bird of prey").

Opinions may vary on whether the Wright Flyer or the 14-bis was the more practical (and thus the "first") heavier-than-air flying machine. Both designs produced aircraft that made free, manned, powered flights. Which one was "first" or "more practical" is a matter of how those words are defined. No one could contest that the Wrights flew first, that the Flyer was more capable in the air, or that Santos Dumont took off on wheels before the Wrights and earned a variety of prizes and official records in France. Patriotic pride heavily influences opinions of the relative importance and practicality of each

aircraft, thus causing debate. U.S. citizens prefer definitions that make the Wrights the "first" to fly, while Brazilians believe that Santos Dumont had the first "real", practical airplane, and that his nationality may have caused his accomplishments to not receive worldwide recognition.

In subsequent years, Santos-Dumont built more aircraft like Demoiselle. He was so enthusiastic about aviation that he released the drawings of Demoiselle for free, thinking that aviation would be the mainstream of a new prosperous era for mankind, and it became the world's first series production aircraft.

Other early flights & claims of flights

Around the years 1900 to 1910, a number of other inventors made or claimed to have made short flights.

Gustave Whitehead's aircraft was represented in a sketch in the Bridgeport Herald.

On August 14, 1901, in Fairfield, Connecticut, Gustave Whitehead reportedly flew his engine-powered No.21 for 800 metres (2,600 ft) at 15 metres (49 ft) height. In January 1902, he claimed to have flown 11 kilometres (6.8 mi) over Long Island Sound in the improved No.22. After 1903, Whitehead faded from public awareness. Three decades later, Whitehead's possible flights emerged from obscurity after the events were featured in a 1935 newspaper article and a 1937 book. Aviation experts debated the topic, and a

few decided for Whitehead, while the great majority, such as Charles Harvard Gibbs-Smith, said the flights could not have occurred.

The first in-flight film, made by a camera man flying with Wilbur Wright on 24 April 1909

Lyman Gilmore claimed to have achieved success on 15 May 1902 and is widely credited with the first use of the word "airport."

In New Zealand, South Canterbury farmer and inventor Richard Pearse constructed a monoplane aircraft that he reputedly flew in early 1903. Good evidence exists that on March 31, 1903 Pearse achieved a powered, though poorly controlled, flight of several hundred metres. Pearse himself said that although he had made a powered takeoff, it was at "too low a speed for [his] controls to work".

The first balloon flights took place in Australia in the late 19th century while Bill Wittber and then escapologist Harry Houdini made Australia's first controlled flights in 1910.. Wittber was conducting taxiing tests in a Blériot XI aircraft in March 1910 in South Australia when he suddenly found himself about five feet in the air (Wittber's Hop). He flew about 40 feet (12 m) before landing. South Australia's other aviation firsts include the first flight from England to Australia by brothers Sir Ross and Sir Keith Smith in their Vickers Vimy bomber, the first Arctic flight by South Australian born Sir Hubert Wilkins and the first Australian born astronaut, Andy Thomas.

Karl Jatho from Hanover conducted a short motorized flight in August 1903, just a few months after Pearse. Jatho's wing design and airspeed did not allow his control surfaces to act properly to control the aircraft.

Also in the summer of 1903, eyewitnesses claimed to have seen Preston Watson make his initial flights at Errol, near Dundee in the east of Scotland. Once again, however, lack of photographic or documentary evidence makes the claim difficult to verify. Many claims

of flight are complicated by the fact that many early flights were done at such low altitude that they did not clear the ground effect, and by the complexities involved in the differences between unpowered and powered aircraft.

The Wright brothers conducted numerous additional flights (about 150) in 1904 and 1905 from Huffman Prairie in Dayton, Ohio and invited friends and relatives. Newspaper reporters did not pay attention after seeing an unsuccessful flight attempt in May 1904.

Public exhibitions of high altitude flights were made by Daniel Maloney in the John Joseph Montgomery tandem-wing glider in March and April 1905 in the Santa Clara, California area. These flights received national media attention and demonstrated superior control of the design, with launches as high as 4,000 feet (1,200 m) and landings made at predetermined locations.

Two English inventors Henry Farman and John William Dunne were also working separately on powered flying machines. In January 1908, Farman won the Grand Prix d'Aviation by flying a 1 km circle, though by this time several longer flights had already been done. For example, the Wright brothers had made a flight over 39 kilometres (24 mi) in October 1905. Dunne's early work was sponsored by the British military, and tested in great secrecy in Glen Tilt in the Scottish Highlands. His best early design, the D4, flew in December 1908 near Blair Atholl in Perthshire. Dunne's main contribution to early aviation was stability, which was a key problem with the planes designed by the Wright brothers and Samuel Cody.

On 14 May 1908 Wilbur Wright piloted the first two-person fixed-wing flight, with Charlie Furnas as a passenger.

On 8 July 1908 Thérèse Peltier became the first woman to fly as a passenger in an airplane when she made a flight of 656 feet (200 m) with Léon Delagrange in Milan, Italy.

Thomas Selfridge became the first person killed in a powered aircraft on 17 September 1908, when Orville Wright crashed his two-passenger plane during military tests at Fort Myer in Virginia.

The first powered flight in Britain was made in 1908 by American Sam Cody in a plane designed and built with the British Army.

In September 1908, Mrs Edith Berg became the first American woman to fly as a passenger in an airplane when she flew with Wilbur Wright in Le Mans, France.

The first powered flight by a Briton in Britain was made by John Moore-Brabazon (JTC Moore Brabazon) in May 1909 on the Isle of Sheppey (Kent).

On 25 July 1909 Louis Blériot flew the Blériot XI monoplane across the English Channel winning the Daily Mail aviation prize. His flight from Calais to Dover lasted 37 minutes.

On 22 October 1909 Raymonde de Laroche became the first woman to fly solo in a powered heavier -than-air craft. She was also the first woman in the world to receive a pilot's licence.

Controversy over who gets credit for invention of the aircraft has been fueled by Pearse's and Jatho's essentially non-existent efforts to inform the popular press and by the Wrights' secrecy while their patent was prepared. For example, the Romanian engineer Traian Vuia (1872–1950) has also been claimed to have built the first self-propelled, heavier-than-air aircraft able to take off autonomously, without a headwind and entirely driven by its own power. Vuia piloted the aircraft he designed and built on 18 March 1906 at Montesson, near Paris. None of his flights were longer than 100 feet (30 m) in length. In comparison, in October 1905, the Wright brothers had a sustained flight of 39 minutes and 24.5 miles (39 km), circling over Huffman Prairie.

Helicopter

In 1877, Enrico Forlanini developed an unmanned helicopter powered by a steam engine. It rose to a height of 13 meters, where it remained for some 20 seconds, after a vertical take-off from a park in Milan.

Paul Cornu's helicopter, built in 1907, was the first manned flying machine to have risen from the ground using rotating wings instead of fixed wings.

The first time a manned helicopter is known to have risen off the ground was in 1907 at Lisenux, France. The first successful rotorcraft, however, wasn't a true helicopter, but an autogyro invented by Spanish engineer Juan de la Cierva in 1919. These kind of rotorcrafts were mainly used until the development of modern helicopters, when, for some reason, they became largely neglected, although the idea has since been resurrected several times. Since the first practical helicopter was the Focke Achgelis Fw 61 (Germany, 1936), the autogyro's golden age only lasted around 20 years.

Seaplane

The first powered seaplane was invented in March 1910 by the French engineer Henri Fabre. Its name was Le Canard ('the duck'), and took off from the water and flew 800 meters on its first flight on March 28, 1910. These experiments were closely followed by the aircraft pioneers Gabriel and Charles Voisin, who purchased several of the Fabre

floats and fitted them to their Canard Voisin airplane. In October 1910, the Canard Voisin became the first seaplane to fly over the river Seine, and in March 1912, the first seaplane to be used militarily from a seaplane carrier, La Foudre ('the lightning').

First performances steps under World War I (1914–1918)

German Taube monoplane, illustration from 1917

Almost as soon as they were invented, planes were drafted for military service. The first country to use planes for military purposes was Italy, whose planes made reconnaissance, bombing and shelling correction military flights during the Italian-Turkish war

(September 1911 – October 1912), in Libya. First mission (a reconnaissance) happened on the 23rd October 1911. First bombing of enemy columns was the 1st November 1911. Then Bulgaria followed this example. Its planes attacked and reconnoitered the Ottoman positions during the First Balkan War 1912–13. The first war to see major use of planes in offensive, defensive and reconnaissance capabilities was World War I. The Allies and Central Powers both used planes extensively.

While the concept of using the aeroplane as a weapon of war was generally laughed at before World War I, the idea of using it for photography was one that was not lost on any of the major forces. All of the major forces in Europe had light aircraft, typically derived from pre-war sporting designs, attached to their reconnaissance departments. Radiotelephones were also being explored on airplanes, notably the SCR-68, as communication between pilots and ground commander grew more and more important

Combat schemes

It was not long before aircraft were shooting at each other, but the lack of any sort of steady point for the gun was a problem. The French solved this problem when, in late 1914, Roland Garros attached a fixed machine gun to the front of his plane, but while Adolphe Pegoud would become known as the first "ace", getting credit for five victories, before also becoming the first ace to die in action, it was German Luftstreitkräfte Leutnant Kurt Wintgens, who, on July 1, 1915, scored the very first aerial victory by a purpose-built fighter plane, with a synchronized machine gun.

Aviators were styled as modern day knights, doing individual combat with their enemies. Several pilots became famous for their air to air combats, the most well known is Manfred von Richthofen, better known as the Red Baron, who shot down 80 planes in air to air combat with several different planes, the most celebrated of which was the Fokker Dr.I. On the Allied side, René Paul Fonck is credited with the most all-time victories at 75, even when later wars are considered.

Because all of the litigations and patent wars fought by the Wright brothers the development of airplanes in USA was hindered and delayed so in WWI practically all pilots, including American pilots, had to use airplanes made in Europe.

Technology and performance advances in aviation's "Golden Age" (1918–1939) The years between World War I and World War II saw great advancements in aircraft technology. Aeroplanes evolved from low-powered biplanes made from wood and fabric to sleek, high-powered monoplanes made of aluminum, based primarily on the founding work of Hugo Junkers during the World War I period. The age of the great airships came and went.

Flagg biplane from 1933.

After WWI experienced fighter pilots were eager to show off their new skills. Many American pilots became barnstormers, flying into small towns across the country and showing off their flying abilities, as well as taking paying passengers for rides. Eventually the barnstormers grouped into more organized displays. Air shows sprang up around the country, with air races, acrobatic stunts, and feats of air superiority. The air races drove engine and airframe development—the Schneider Trophy, for example, led to a series of ever faster and sleeker monoplane designs culminating in the Supermarine S.6B, a direct forerunner of the Spitfire. With pilots competing for cash prizes, there was an incentive to go faster. Amelia Earhart was perhaps the most famous of those on the barnstorming/air show circuit. She was also the first female pilot to achieve records such as crossing of the Atlantic and Pacific Oceans.

Qantas De Havilland biplane, ca. 1930

Other prizes, for distance and speed records, also drove development forwards. For example on June 14, 1919, Captain John Alcock and Lieutenant Arthur Brown co-piloted a Vickers Vimy non-stop from St. John's, Newfoundland to Clifden, Ireland, winning the £13,000 ($65,000) Northcliffe prize. Eight years later Charles Lindbergh took the Orteig Prize of $25,000 for the first solo non-stop crossing of the Atlantic.

Australian Charles Kingsford Smith was the first to fly across the larger Pacific Ocean in the Southern Cross. His crew left Oakland, California to make the first trans-Pacific flight to Australia in three stages. The first (from Oakland to Hawaii) was 2,400 miles, took 27 hours 25 minutes and was uneventful. They then flew to Suva, Fiji 3,100 miles away, taking 34 hours 30 minutes. This was the toughest part of the journey as they flew through a massive lightning storm near the equator. They then flew on to Brisbane in 20 hours, where they landed on 9 June 1928 after approximately 7,400 miles total flight. On arrival, Kingsford Smith was met by a huge crowd of 25,000 at Eagle Farm Airport in his hometown of Brisbane. Accompanying him were Australian aviator Charles Ulm as the relief pilot, and the Americans James Warner and Captain Harry Lyon (who were the radio operator, navigator and engineer). With Ulm, Kingsford Smith later continued his journey being the first in 1929 to circumnavigate the world, crossing the equator twice.

The first lighter-than-air crossings of the Atlantic were made by airship in July 1919 by His Majesty's Airship R34 and crew when they flew from East Lothian, Scotland to Long Island, New York and then back to Pulham, England. By 1929, airship technology had advanced to the point that the first round-the-world flight was completed by the Graf Zeppelin in September and in October, the same aircraft inaugurated the first commercial transatlantic service. However the age of the dirigible ended following the destruction by fire of the zeppelin Hindenburg just before landing at Lakehurst, New Jersey on May 6,

1937, killing 35 of the 97 people aboard. Previous spectacular airship accidents, from the Wingfoot Express disaster (1919) to the loss of the Akron (1933) and the Macon (1935) had already cast doubt on airship safety; following the destruction of the Hindenburg, the remaining airship making international flights, the Graf Zeppelin was retired (June 1937); its replacement, the dirigible Graf Zeppelin II, made a number of flights, primarily over Germany, from 1938 to 1939, but was grounded when Germany began World War II. Both remaining German zeppelins were scrapped in 1940 to supply metal for the German Luftwaffe; the last American zeppelin, the Los Angeles, which had not flown since 1932, was dismantled in late 1939.

Meanwhile in Germany, who was restricted by the Treaty of Versailles in its development of powered aircraft, instead developed gliding as a sport, especially at the Wasserkuppe, during the 1920s. In its various forms, this activity now has over 400,000 participants.

In 1929 Jimmy Doolittle developed instrument flight.

1929 also saw the first flight of by far the largest plane ever built until then: the Dornier Do X with a wing span of 48 m. On its 70th test flight on October 21 there were 169 people on board, a record that was not broken for 20 years.

In the 1930s development of the jet engine began in Germany and in England. In England Frank Whittle patented a design for a jet engine in 1930 and towards the end of the decade began developing an engine. In Germany Hans von Ohain patented his version of a jet engine in 1936 and began developing a similar engine. The two men were unaware of the other's work, and both Germany and Britain would go on to develop jet aircraft by the end of World War II.

Progress goes on and massive production, World War II (1939–1945) World War II saw a drastic increase in the pace of aircraft development and production. All countries involved in the war stepped up development and production of aircraft and flight based weapon delivery systems, such as the first long range bomber. Also air combat tactics and doctrines changed, large scale strategic bombing campaigns were launched, Fighter escorts introduced and the more flexible aircraft and weapons allowed more precise attacks on small targets for effective ground support. New technologies like radar also allowed more coordinated and controlled deployment of fighter aircraft.

Me 262, world first operational jet fighter

The first functional jetplane was the Heinkel He 178 (Germany), flown by Erich Warsitz in 1939, followed by the worlds first operational fighter aircraft, the Me 262, in July 1942 and worlds first jet powered bomber, the Arado Ar 234, in June 1943. British developments, like the Gloster Meteor, followed afterwards, but saw only brief use in World War II. The first cruise missile (V-1), the first ballistic missile (V-2), the first (and to date only) operational rocket powered combat aircraft Me 163 and the first vertical take-off manned point-defense interceptor Bachem Ba 349 were also developed by Germany. However, jet fighters had only limited impact due to their late introduction, fuel shortages, the lack of experienced pilots and the declining war industry of Germany.

But not only airplanes, helicopters too saw rapid development in the Second World War. With the introduction of the Focke Achgelis Fa 223, the Flettner Fl 282 in 1941 in Germany and the Sikorsky R-4 1942 in the USA, the first time larger helicopter formations were produced and deployed.

1945–1991: The Cold War

D.H. Comet, the world's first jet airliner. As in this picture, it also saw RAF service

A 1945 newsreel covering various firsts in human flight

After World War II, commercial aviation grew rapidly, used mostly ex-military aircraft to transport people and cargo. This growth was accelerated by the glut of heavy and super-heavy bomber airframes like the B-29 and Lancaster that could be converted into commercial aircraft. The DC-3 also made for easier and longer commercial flights. The first commercial jet airliner to fly was the British De Havilland Comet. By 1952, the British state airline BOAC had introduced the De Havilland Comet into scheduled service. While a technical achievement, the plane suffered a series of highly public failures, as the shape of the windows led to cracks due to metal fatigue. The fatigue was caused by cycles of pressurization and depressurization of the cabin, and eventually led to catastrophic failure of the plane's fuselage. By the time the problems were overcome, other jet airliner designs had already taken to the skies.

USSR's Aeroflot became the first airline in the world to operate sustained regular jet services on September 15, 1956 with the Tupolev Tu-104. Boeing 707, which established new levels of comfort, safety and passenger expectations, ushered in the age of mass commercial air travel, dubbed the Jet Age.

In October 1947 Chuck Yeager took the rocket powered Bell X-1 past the speed of sound. Although anecdotal evidence exists that some fighter pilots may have done so while divebombing ground targets during the war, this was the first controlled, level flight to cross the sound barrier. Further barriers of distance fell in 1948 and 1952 with the first jet crossing of the Atlantic and the first nonstop flight to Australia.

When the Soviet Union developed long-range bombers that could deliver nuclear weapons to North America and Europe, Western countries responded with interceptor aircraft that could engage and destroy the bombers before they reached their destination. The "minister-of-everything" C.D. Howe in the Canadian government, was the key proponent of the Avro Arrow, designed as a high-speed interceptor, reputedly the fastest aircraft in its time. However, by 1955, most Western countries agreed that the interceptor age was replaced by guided missile age. Consequently, the Avro Arrow project was eventually cancelled in 1959 under Prime Minister John Diefenbaker.

In 1961, the sky was no longer the limit for manned flight, as Yuri Gagarin orbited once around the planet within 108 minutes, and then used the descent module of Vostok I to safely reenter the atmosphere and reduce speed from Mach 25 using friction and converting velocity into heat. This action further heated up the space race that had started in 1957 with the launch of Sputnik 1 by the Soviet Union. The United States responded by launching Alan Shepard into space on a suborbital flight in a Mercury space capsule. With the launch of the Alouette I in 1963, Canada became the third country to send a satellite in space. The Space race between the United States and the Soviet Union would ultimately lead to the landing of men on the moon in 1969.

In 1967, the X-15 set the air speed record for an aircraft at 4,534 mph (7,297 km/h) or Mach 6.1 (7,297 km/h). Aside from vehicles designed to fly in outer space, this record was renewed by X-43 in the 21st century.

Apollo 11 lifts off on its mission to land a man on the moon

The Harrier Jump Jet, often referred to as just "Harrier" or "the Jump Jet", is a British designed military jet aircraft capable of Vertical/Short Takeoff and Landing (V/STOL) via thrust vectoring. It first flew in 1969. The same year that Neil Armstrong and Buzz Aldrin set foot on the moon, and Boeing unveiled the Boeing 747 and the Aérospatiale-BAC Concorde supersonic passenger airliner had its maiden flight. The 747 plane was the largest aircraft ever to fly, and still carries millions of passengers each year, though it has been superseded by the Airbus A380, which is capable of carrying up to 853 passengers. In 1975 Aeroflot started regular service on the Tu-144—the first supersonic passenger plane. In 1976 British Airways began supersonic service across the Atlantic, with Concorde. A few years earlier the SR-71 Blackbird had set the record for crossing the Atlantic in under 2 hours, and Concorde followed in its footsteps.

The last quarter of the 20th century saw a slowing of the pace of advancement. No longer was revolutionary progress made in flight speeds, distances and technology. This part of the century saw the steady improvement of flight avionics, and a few minor milestones in flight progress.

For example, in 1979 the Gossamer Albatross became the first human powered aircraft to cross the English channel. This achievement finally saw the realization of centuries of dreams of human flight. In 1981, the Space Shuttle made its first orbital flight, proving that a large rocket ship can take off into space, provide a pressurised life support system for several days, reenter the atmosphere at orbital speed, precision glide to a runway and land like a plane.

In 1986 Dick Rutan and Jeana Yeager flew an aircraft, the Rutan Voyager, around the world unrefuelled, and without landing. In 1999 Bertrand Piccard became the first person to circle the earth in a balloon. Focus was turning to the ultimate conquest of space and flight at faster than the speed of sound. The ANSARI X PRIZE inspired entrepreneurs and space enthusiasts to build their own rocket ships to fly faster than sound and climb into the lower reaches of space.

2001–present

Concorde, G-BOAB, in storage at London Heathrow Airport following the end of all Concorde flying. This aircraft flew for 22,296 hours between its first flight in 1976 and final flight in 2000.

In commercial aviation, the early 21st century saw the end of an era with the retirement of Concorde. Supersonic flight was not commercially viable, as the planes were required to fly over the oceans if they wanted to break the sound barrier. Concorde also was fuel

hungry and could carry a limited amount of passengers due to its highly streamlined design. Nevertherless, it seems to have made a significant operating profit for British Airways.

In the beginning of the 21st century, subsonic military aviation focused on eliminating the pilot in favor of remotely operated or completely autonomous vehicles. Several unmanned aerial vehicles or UAVs have been developed. In April 2001 the unmanned aircraft Global Hawk flew from Edwards AFB in the US to Australia non-stop and unrefuelled. This is the longest point-to-point flight ever undertaken by an unmanned aircraft, and took 23 hours and 23 minutes. In October 2003 the first totally autonomous flight across the Atlantic by a computer-controlled model aircraft occurred.

The U.S. Centennial of Flight Commission was established in 1999 to encourage the broadest national and international participation in the celebration of 100 years of powered flight. It publicized and encouraged a number of programs, projects and events intended to educate people about the history of aviation.

Major disruptions to air travel in the 21st Century included the closing of U.S. airspace due to the September 11 attacks, and the closing of northern European airspace after the 2010 eruption of Eyjafjallajökull.

Chapter 3

Elements of Aerospace Engineering

1. Fluid mechanics Fluid mechanics is the study of fluids and the forces on them. (Fluids include liquids, gases, and plasmas.) Fluid mechanics can be divided into fluid kinematics, the study of fluid motion, and fluid dynamics, the study of the effect of forces on fluid motion, which can further be divided into fluid statics, the study of fluids at rest, and fluid kinetics, the study of fluids in motion. It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms, that is, it models matter from a macroscopic viewpoint rather than from a microscopic viewpoint. Fluid mechanics, especially fluid dynamics, is an active field of research with many unsolved or partly solved problems. Fluid mechanics can be mathematically complex. Sometimes it can best be solved by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach to solving fluid mechanics problems. Also taking advantage of the highly visual nature of fluid flow is particle image velocimetry, an experimental method for visualizing and analyzing fluid flow.

Brief history The study of fluid mechanics goes back at least to the days of ancient Greece, when Archimedes investigated fluid statics and buoyancy and formulated his famous law known now as the Archimedes Principle. Rapid advancement in fluid mechanics began with Leonardo da Vinci (observation and experiment), Evangelista Torricelli (barometer), Isaac Newton (viscosity) and Blaise Pascal (hydrostatics), and was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in Hydrodynamica (1738). Inviscid flow was further analyzed by various mathematicians (Leonhard Euler, d'Alembert, Lagrange, Laplace, Poisson) and viscous flow was explored by a multitude of engineers including Poiseuille and Gotthilf Heinrich Ludwig Hagen. Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations, and boundary layers were investigated (Ludwig Prandtl), while various scientists (Osborne Reynolds, Andrey Kolmogorov, Geoffrey Ingram Taylor) advanced the understanding of fluid viscosity and turbulence.

Relationship to continuum mechanics Fluid mechanics is a subdiscipline of continuum mechanics, as illustrated in the following table.

Continuum mechanics The study of the physics of continuous materials

Solid mechanics The study of the physics of continuous materials with a defined rest shape.

Elasticity Describes materials that return to their rest shape after an applied stress. Plasticity Describes materials that permanently deform after a sufficient applied stress.

Rheology The study of materials with both solid and fluid characteristics.

Fluid mechanics The study of the physics of continuous materials which take the shape of their container.

Non-Newtonian fluids

Newtonian fluids

In a mechanical view, a fluid is a substance that does not support shear stress; that is why a fluid at rest has the shape of its containing vessel. A fluid at rest has no shear stress.

Assumptions Like any mathematical model of the real world, fluid mechanics makes some basic assumptions about the materials being studied. These assumptions are turned into equations that must be satisfied if the assumptions are to be held true. For example, consider an incompressible fluid in three dimensions. The assumption that mass is conserved means that for any fixed closed surface (such as a sphere) the rate of mass passing from outside to inside the surface must be the same as rate of mass passing the other way. (Alternatively, the mass inside remains constant, as does the mass outside). This can be turned into an integral equation over the surface.

Fluid mechanics assumes that every fluid obeys the following:

• Conservation of mass • Conservation of energy • Conservation of momentum • The continuum hypothesis, detailed below.

Further, it is often useful (at subsonic conditions) to assume a fluid is incompressible – that is, the density of the fluid does not change. Liquids can often be modelled as incompressible fluids, whereas gases cannot.

Similarly, it can sometimes be assumed that the viscosity of the fluid is zero (the fluid is inviscid). Gases can often be assumed to be inviscid. If a fluid is viscous, and its flow contained in some way (e.g. in a pipe), then the flow at the boundary must have zero

velocity. For a viscous fluid, if the boundary is not porous, the shear forces between the fluid and the boundary results also in a zero velocity for the fluid at the boundary. This is called the no-slip condition. For a porous media otherwise, in the frontier of the containing vessel, the slip condition is not zero velocity, and the fluid has a discontinuous velocity field between the free fluid and the fluid in the porous media (this is related to the Beavers and Joseph condition).

The continuum hypothesis

Fluids are composed of molecules that collide with one another and solid objects. The continuum assumption, however, considers fluids to be continuous. That is, properties such as density, pressure, temperature, and velocity are taken to be well-defined at "infinitely" small points, defining a REV (Reference Element of Volume), at the geometric order of the distance between two adjacent molecules of fluid. Properties are assumed to vary continuously from one point to another, and are averaged values in the REV. The fact that the fluid is made up of discrete molecules is ignored.

The continuum hypothesis is basically an approximation, in the same way planets are approximated by point particles when dealing with celestial mechanics, and therefore results in approximate solutions. Consequently, assumption of the continuum hypothesis can lead to results which are not of desired accuracy. That said, under the right circumstances, the continuum hypothesis produces extremely accurate results.

Those problems for which the continuum hypothesis does not allow solutions of desired accuracy are solved using statistical mechanics. To determine whether or not to use conventional fluid dynamics or statistical mechanics, the Knudsen number is evaluated for the problem. The Knudsen number is defined as the ratio of the molecular mean free path length to a certain representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. (More simply, the Knudsen number is how many times its own diameter a particle will travel on average before hitting another particle). Problems with Knudsen numbers at or above unity are best evaluated using statistical mechanics for reliable solutions.

Navier–Stokes equations The Navier–Stokes equations (named after Claude-Louis Navier and George Gabriel Stokes) are the set of equations that describe the motion of fluid substances such as liquids and gases. These equations state that changes in momentum (force) of fluid particles depend only on the external pressure and internal viscous forces (similar to friction) acting on the fluid. Thus, the Navier–Stokes equations describe the balance of forces acting at any given region of the fluid.

The Navier–Stokes equations are differential equations which describe the motion of a fluid. Such equations establish relations among the rates of change of the variables of interest. For example, the Navier–Stokes equations for an ideal fluid with zero viscosity

states that acceleration (the rate of change of velocity) is proportional to the derivative of internal pressure.

This means that solutions of the Navier–Stokes equations for a given physical problem must be sought with the help of calculus. In practical terms only the simplest cases can be solved exactly in this way. These cases generally involve non-turbulent, steady flow (flow does not change with time) in which the Reynolds number is small.

For more complex situations, such as global weather systems like El Niño or lift in a wing, solutions of the Navier–Stokes equations can currently only be found with the help of computers. This is a field of sciences by its own called computational fluid dynamics.

General form of the equation

The general form of the Navier–Stokes equations for the conservation of momentum is:

where

• is the fluid density,

• is the substantive derivative (also called the material derivative), • is the velocity vector, • is the body force vector, and • is a tensor that represents the surface forces applied on a fluid particle (the

comoving stress tensor).

Unless the fluid is made up of spinning degrees of freedom like vortices, is a symmetric tensor. In general, (in three dimensions) has the form:

where

• are normal stresses, • are tangential stresses (shear stresses).

The above is actually a set of three equations, one per dimension. By themselves, these aren't sufficient to produce a solution. However, adding conservation of mass and appropriate boundary conditions to the system of equations produces a solvable set of equations.

Newtonian versus non-Newtonian fluids A Newtonian fluid (named after Isaac Newton) is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. This definition means regardless of the forces acting on a fluid, it continues to flow. For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the drag of a small object being moved slowly through the fluid is proportional to the force applied to the object. (Compare friction). Important fluids, like water as well as most gases, behave — to good approximation — as a Newtonian fluid under normal conditions on Earth.

By contrast, stirring a non-Newtonian fluid can leave a "hole" behind. This will gradually fill up over time – this behaviour is seen in materials such as pudding, oobleck, or sand (although sand isn't strictly a fluid). Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" (this is seen in non-drip paints). There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property — for example, most fluids with long molecular chains can react in a non-Newtonian manner.

Equations for a Newtonian fluid

The constant of proportionality between the shear stress and the velocity gradient is known as the viscosity. A simple equation to describe Newtonian fluid behaviour is

where

τ is the shear stress exerted by the fluid ("drag") μ is the fluid viscosity – a constant of proportionality

is the velocity gradient perpendicular to the direction of shear.

For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure, not on the forces acting upon it. If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress (in Cartesian coordinates) is

where

τij is the shear stress on the ith face of a fluid element in the jth direction vi is the velocity in the ith direction xj is the jth direction coordinate.

If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types.

Among fluids, two rough broad divisions can be made: ideal and non-ideal fluids. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. An Ideal fluid is non viscous- offers no resistance whatsoever to a shearing force.

One can group real fluids into Newtonian and non-Newtonian. Newtonian fluids agree with Newton's law of viscosity. Non-Newtonian fluids can be either plastic, bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelatic.

2. Control engineering

Control systems play a critical role in space flight

Control engineering or Control systems engineering is the engineering discipline that applies control theory to design systems with predictable behaviors. The practice uses sensors to measure the output performance of the device being controlled (often a vehicle) and those measurements can be used to give feedback to the input actuators that can make corrections toward desired performance. When a device is designed to perform without the need of human inputs for correction it is called automatic control (such as cruise control for regulating a car's speed). Multi-disciplinary in nature, control systems engineering activities focus on implementation of control systems mainly derived by mathematical modeling of systems of a diverse range.

Overview Modern day control engineering (also called control systems engineering) is a relatively new field of study that gained a significant attention during 20th century with the advancement in technology. It can be broadly defined as practical application of control theory. Control engineering has an essential role in a wide range of control systems, from simple household washing machines to high-performance F-16 fighter aircraft. It seeks to understand physical systems, using mathematical modeling, in terms of inputs, outputs and various components with different behaviors; use control systems design tools to develop controllers for those systems; and implement controllers in physical systems employing available technology. A system can be mechanical, electrical, fluid, chemical, financial and even biological, and the mathematical modeling, analysis and controller design uses control theory in one or many of the time, frequency and complex-s domains, depending on the nature of the design problem.

History Automatic control Systems were first developed over two thousand years ago. The first feedback control device on record is thought to be the ancient water clock of Ktesibios in Alexandria Egypt around the third century B.C. It kept time by regulating the water level in a vessel and, therefore, the water flow from that vessel. This certainly was a successful device as water clocks of similar design were still being made in ~Baghdad when the Mongols captured the city in 1258 A.D. A variety of automatic devices have been used over the centuries to accomplish useful tasks or simply to just entertain. The latter includes the automata, popular in Europe in the 17th and 18th centuries, featuring dancing figures that would repeat the same task over and over again; these automata are examples of open-loop control. Milestones among feedback, or "closed-loop" automatic control devices, include the temperature regulator of a furnace attributed to Drebbel, circa 1620, and the centrifugal flyball governor used for regulating the speed of steam engines by James Watt in 1788.

In his 1868 paper "On Governors", J. C. Maxwell (who discovered the Maxwell electromagnetic field equations) was able to explain instabilities exhibited by the flyball governor using differential equations to describe the control system. This demonstrated the importance and usefulness of mathematical models and methods in understanding

complex phenomena, and signaled the beginning of mathematical control and systems theory. Elements of control theory had appeared earlier but not as dramatically and convincingly as in Maxwell's analysis.

Control theory made significant strides in the next 100 years. New mathematical techniques made it possible to control, more accurately, significantly more complex dynamical systems than the original flyball governor. These techniques include developments in optimal control in the 1950s and 1960s, followed by progress in stochastic, robust, adaptive and optimal control methods in the 1970s and 1980s. Applications of control methodology have helped make possible space travel and communication satellites, safer and more efficient aircraft, cleaner auto engines, cleaner and more efficient chemical processes, to mention but a few.

Before it emerged as a unique discipline, control engineering was practiced as a part of mechanical engineering and control theory was studied as a part of electrical engineering, since electrical circuits can often be easily described using control theory techniques. In the very first control relationships, a current output was represented with a voltage control input. However, not having proper technology to implement electrical control systems, designers left with the option of less efficient and slow responding mechanical systems. A very effective mechanical controller that is still widely used in some hydro plants is the governor. Later on, previous to modern power electronics, process control systems for industrial applications were devised by mechanical engineers using pneumatic and hydraulic control devices, many of which are still in use today.

Control theory There are two major divisions in control theory, namely, classical and modern, which have direct implications over the control engineering applications. The scope of classical control theory is limited to single-input and single-output (SISO) system design. The system analysis is carried out in time domain using differential equations, in complex-s domain with Laplace transform or in frequency domain by transforming from the complex-s domain. All systems are assumed to be second order and single variable, and higher-order system responses and multivariable effects are ignored. A controller designed using classical theory usually requires on-site tuning due to design approximations. Yet, due to easier physical implementation of classical controller designs as compared to systems designed using modern control theory, these controllers are preferred in most industrial applications. The most common controllers designed using classical control theory are PID controllers.

In contrast, modern control theory is carried out strictly in the complex-s or the frequency domain, and can deal with multi-input and multi-output (MIMO) systems. This overcomes the limitations of classical control theory in more sophisticated design problems, such as fighter aircraft control. In modern design, a system is represented as a set of first order differential equations defined using state variables. Nonlinear, multivariable, adaptive and robust control theories come under this division. Being fairly new, modern control theory has many areas yet to be explored. Scholars like Rudolf E.

Kalman and Aleksandr Lyapunov are well-known among the people who have shaped modern control theory.

Control systems Control engineering is the engineering discipline that focuses on the modeling of a diverse range of dynamic systems (e.g. mechanical systems) and the design of controllers that will cause these systems to behave in the desired manner. Although such controllers need not be electrical many are and hence control engineering is often viewed as a subfield of electrical engineering. However, the falling price of microprocessors is making the actual implementation of a control system essentially trivial. As a result, focus is shifting back to the mechanical engineering discipline, as intimate knowledge of the physical system being controlled is often desired.

Electrical circuits, digital signal processors and microcontrollers can all be used to implement Control systems. Control engineering has a wide range of applications from the flight and propulsion systems of commercial airliners to the cruise control present in many modern automobiles.

In most of the cases, control engineers utilize feedback when designing control systems. This is often accomplished using a PID controller system. For example, in an automobile with cruise control the vehicle's speed is continuously monitored and fed back to the system which adjusts the motor's torque accordingly. Where there is regular feedback, control theory can be used to determine how the system responds to such feedback. In practically all such systems stability is important and control theory can help ensure stability is achieved.

Although feedback is an important aspect of control engineering, control engineers may also work on the control of systems without feedback. This is known as open loop control. A classic example of open loop control is a washing machine that runs through a pre-determined cycle without the use of sensors.

Control engineering education At many universities, control engineering courses are taught in Electrical and Electronic Engineering, Mechatronics Engineering, Mechanical engineering, and Aerospace engineering; in others it is connected to computer science, as most control techniques today are implemented through computers, often as Embedded systems (as in the automotive field). The field of control within chemical engineering is often known as process control. It deals primarily with the control of variables in a chemical process in a plant. It is taught as part of the undergraduate curriculum of any chemical engineering program, and employs many of the same principles in control engineering. Other engineering disciplines also overlap with control engineering, as it can be applied to any system for which a suitable model can be derived.

Control engineering has diversified applications that include science, finance management, and even human behavior. Students of control engineering may start with a linear control system course dealing with the time and complex-s domain, which requires a thorough background in elementary mathematics and Laplace transform (called classical control theory). In linear control, the student does frequency and time domain analysis. Digital control and nonlinear control courses require z transformation and algebra respectively, and could be said to complete a basic control education. From here onwards there are several sub branches.

Recent advancement Originally control engineering was all about continuous systems. Development of computer control tools posed a requirement of discrete control system engineering because the communications between the computer-based digital controller and the physical system are governed by a computer clock. The equivalent to Laplace transform in the discrete domain is the z-transform. Today many of the control systems are computer controlled and they consist of both digital and analogue components.

Therefore, at the design stage either digital components are mapped into the continuous domain and the design is carried out in the continuous domain, or analogue components are mapped in to discrete domain and design is carried out there. The first of these two methods is more commonly encountered in practice because many industrial systems have many continuous systems components, including mechanical, fluid, biological and analogue electrical components, with a few digital controllers.

Similarly, the design technique has progressed from paper-and-ruler based manual design to computer-aided design, and now to computer-automated design (CAutoD), which has been made possible by evolutionary computation. CAutoD can be applied not just to tuning a predefined control scheme, but also to controller structure optimisation, system identification and invention of novel control systems, based purely upon a performance requirement, independent of any specific control scheme.

3. Fixed-wing aircraft

PZL-104M Wilga 2000 of Polish Border Guard. This fixed-wing aircraft is notable for its full-span fixed aerodynamic slot on the leading edge of its wing.

A fixed-wing aircraft, typically called an airplane, aeroplane or just plane, is an aircraft capable of flight using forward motion that generates lift as the wing moves through the air. Planes include jet engine and propeller driven vehicles propelled forward by thrust, as well as unpowered aircraft (such as gliders), which use thermals, or warm-air pockets to inherit lift. Fixed-wing aircraft are distinct from ornithopters in which lift is generated by flapping wings and rotary-wing aircraft in which wings rotate about a fixed mast.

Most fixed-wing aircraft are flown by a pilot on board the aircraft, but some are designed to be remotely or computer controlled.

Etymology First attested in English in late 19th century, the word aeroplane derives from the French "aéroplane", which comes from the Greek "ἀήρ" (aēr), "air" + "πλάνος" (planos), "wandering". An ancient Greek term coined from these two words is "ἀερόπλανος" (aeroplanos), "wandering in air".

In the United Kingdom and most of the Commonwealth, the term "aeroplane" is used. In the United States and Canada, the term "airplane" is applied to these aircraft. The form

"aeroplane" is the older of the two, dating back to the mid- to late-19th century. The spelling "airplane" was first recorded in 1907.

History Heavier-than-air flying machines are impossible. —Lord Kelvin

The dream of flight goes back to the days of pre-history. Many stories from antiquity involve flight, such as the Greek legend of Icarus and Daedalus, and the Vimana in ancient Indian epics. Around 400 BC, Archytas, the Ancient Greek philosopher, mathematician, astronomer, statesman, and strategist, was reputed to have designed and built the first artificial, self-propelled flying device, a bird-shaped model propelled by a jet of what was probably steam, said to have actually flown some 200 m. This machine, which its inventor called The Pigeon (Greek: η Περιστέρα "hè Peristera"), may have been suspended on a wire or pivot for its flight. One of the first recorded – still dilettante – attempts with gliders were those by the 11th century monk Eilmer of Malmesbury (recorded in the 12th century) and the 9th century poet Abbas Ibn Firnas (recorded in the 17th century); both experiments ended with lasting injuries to their pilots. Leonardo da Vinci researched the wing design of birds and designed a man-powered aircraft in his Codex on the Flight of Birds (1502). In the 18th century, Francois Pilatre de Rozier and François Laurent d'Arlandes flew in an aircraft lighter than air, a balloon. The biggest challenge became to create other craft, capable of controlled flight.

Le Bris and his glider, Albatros II, photographed by Nadar, 1868.

Sir George Cayley, the founder of the science of aerodynamics, credited as the first person to separate the forces of lift and drag which are in effect on any flight vehicle, in 1799 he set forth the concept of the modern aeroplane as a fixed-wing flying machine with separate systems for lift, propulsion, and control. Cayley was building and flying models of fixed-wing aircraft as early as 1803, and he built a successful passenger-carrying glider in 1853. In 1856, Frenchman Jean-Marie Le Bris made the first powered flight, by having his glider "L'Albatros artificiel" pulled by a horse on a beach. On 28 August 1883, the American John J. Montgomery made a controlled flight in a glider. Other aviators who made similar flights at that time were Otto Lilienthal, Percy Pilcher and Octave Chanute.

The first self-powered fixed-wing aircraft was created by Englishman John Stringfellow, whose unmanned model made its first successful flight in 1848. Alberto Santos-Dumont, a Brazilian living in France, built the first practical dirigible balloons at the end of the nineteenth century. In the 1890s, Australian inventor and aviator Lawrence Hargrave conducted research on wing structures and developed a box kite that lifted the weight of a man. His box kite designs were widely adopted and became the prevalent type of aircraft until 1909. Although he also developed a type of rotary aircraft engine, he did not create and fly a powered fixed-wing aircraft.

On 14 August 1901, in Fairfield, Connecticut, Gustave Whitehead reportedly flew his engine-powered Number 21 aeroplane for half a mile at 15 m height, according to an article in the Bridgeport Sunday Herald. No photographs were taken, but a sketch of the plane in the air was published with the article.

The Wright brothers made their first successful test flights on 17 December 1903. Their flights are recognised by the Fédération Aéronautique Internationale (FAI), the standard setting and record-keeping body for aeronautics and astronautics, as "the first sustained and controlled heavier-than-air powered flight". By 1905, the Wright Flyer III was capable of fully controllable, stable flight for substantial periods.

On 12 November 1906, Santos-Dumont made what Brazilians say was the first airplane flight unassisted by catapult and set the first world record recognised by the Aéro-Club de France by flying 220 metres (720 ft) in less than 22 seconds. This flight was also certified by the Fédération Aéronautique Internationale (FAI).

World War I served as a testbed for the use of the aircraft as a weapon. Initially seen by the generals as a "toy", aircraft demonstrated their potential as mobile observation platforms, then proved themselves to be machines of war capable of causing casualties to the enemy. The earliest known aerial victory with a synchronised machine gun-armed fighter aircraft occurred on July 1, 1915, by German Luftstreitkräfte Leutnant Kurt Wintgens. "Fighter aces" appeared, described as "knights of the air"; the greatest (by number of air victories) was the German Manfred von Richthofen, the Red Baron. On the side of the allies, the ace with the highest number of downed aircraft was René Fonck, of France. All-metal-structure aircraft took their first steps into reality during the World War I era, through the work of Hugo Junkers in the creation of the Junkers J 1 in 1915.

Following the war, aircraft technology continued to develop. Alcock and Brown crossed the Atlantic non-stop for the first time in 1919, a feat first performed solo by Charles Lindbergh in 1927. The first commercial flights took place between the United States and Canada in 1919. The turbine or the jet engine was in development in the 1930s; military jet aircraft began operating in the 1940s.

Aircraft played a primary role in the Second World War, having a presence in all the major battles of the war: Pearl Harbor, the battles of the Pacific, the Battle of Britain. They were an essential component of the military strategies of the period, such as the German Blitzkrieg or the American and Japanese aircraft carrier campaigns of the Pacific.

In October 1947, Chuck Yeager was the first person to exceed the speed of sound, flying the Bell X-1.

Aircraft in a civil military role continued to feed and supply Berlin in 1948, when access to rail roads and roads to the city, completely surrounded by Eastern Germany, were blocked, by order of the Soviet Union.

The Cold War played a large role in the production of new aircraft, such as the B-52

The first commercial jet, the de Havilland Comet, was introduced in 1952. The Boeing 707, the first widely successful commercial jet, was in commercial service for more than 50 years, from October 26, 1958 to June 22, 2010. The Boeing 727 was another widely used passenger aircraft, and the Boeing 747 was the world's biggest commercial aircraft between 1970 and 2005, when it was surpassed by the Airbus A380.

Overview

Structure

The Tupolev Tu-160, a supersonic, variable-geometry heavy bomber

The P-38 Lightning, a twin-engine fixed-wing aircraft with a twin-boom configuration.

A Sukhoi Su-27UB of the Russian Knights aerobatic team showing two vertical stabilisers

An F-16 Fighting Falcon, a US military fixed-wing aircraft

The Mexican unmanned aerial vehicle S4 Ehécatl at take-off

A Boeing KC-135 Stratotanker refueling an F-15 Eagle. The KC-135 holds the record for the longest military service.

Some varieties of aircraft, such as flying wing aircraft, may lack a discernible fuselage structure and horizontal or vertical stabilisers, however the structure of a fixed-winged aircraft usually consists of the following major parts:

• A long narrow, cylindrical, spherical, odd shaped, form, called a fuselage, usually with tapered or rounded ends to make its shape aerodynamically smooth. The fuselage carries the human flight crew if the aircraft is piloted, the passengers if the aircraft is a passenger aircraft, other cargo or payload, and engines and/or fuel if the aircraft is so equipped. The pilots operate the aircraft from a cockpit located at the front or top of the fuselage and equipped with windows, controls, and instruments. Passengers and cargo occupy the remaining available space in the fuselage. Some aircraft may have two fuselages, or additional pods or booms.

• A wing (or wings in a multiplane) with an airfoil cross-section shape, used to generate aerodynamic lifting force to support the aircraft in flight by deflecting air downward as the aircraft moves forward. The wing halves are typically symmetrical about the plane of symmetry (for symmetrical aircraft). The wing also stabilises the aircraft about its roll axis and the ailerons control rotation about that axis.

• At least one control surface (or surfaces) mounted vertically usually above the rear of the fuselage, called a vertical stabiliser. The vertical stabiliser is used to stabilise the aircraft about its yaw axis (the axis in which the aircraft turns from side to side) and to control its rotation along that axis. Some aircraft have multiple vertical stabilisers.

• At least one horizontal surface at the front or back of the fuselage used to stabilise the aircraft about its pitch axis (the axis around which the aircraft tilts upward or downward). The horizontal stabiliser (also known as tailplane) is usually mounted near the rear of the fuselage, or at the top of the vertical stabiliser, or sometimes a canard is mounted near the front of the fuselage for the same purpose.

• On powered aircraft, one or more aircraft engines are propulsion units that provide thrust to push the aircraft forward through the air. The engine is optional in the case of gliders that are not motor gliders. The most common propulsion units are propellers, powered by reciprocating or turbine engines, jet engines or even rocket motors, which provide thrust directly from the engine and usually also from a large fan mounted within the engine. When the number of engines is even, they are distributed symmetrically about the roll axis of the aircraft, which lies along the plane of symmetry (for symmetrical aircraft); when the number is odd, the odd engine is usually mounted along the centreline of the fuselage.

• Landing gear, a set of wheels, skids, or floats that support the aircraft while it is on the surface.

Controls

A number of controls allow pilots to direct aircraft in the air. The controls found in a typical fixed-wing aircraft are as follows:

• A yoke or joystick, which controls rotation of the aircraft about the pitch and roll axes. A yoke resembles a kind of steering wheel, and a control stick is just a simple rod with a handgrip. The pilot can pitch the aircraft downward by pushing on the yoke or stick, and pitch the aircraft upward by pulling on it. Rolling the aircraft is accomplished by turning the yoke in the direction of the desired roll, or by tilting the control stick in that direction. Pitch changes are used to adjust the altitude and speed of the aircraft; roll changes are used to make the aircraft turn. Control sticks and yokes are usually positioned between the pilot's legs; however, a sidestick is a type of control stick that is positioned on either side of the pilot (usually the left side for the pilot in the left seat, and vice versa, if there are two pilot seats).

• Rudder pedals, which control rotation of the aircraft about the yaw axis. There are two pedals that pivot so that when one is pressed forward the other moves backward, and vice versa. The pilot presses on the right rudder pedal to make the aircraft yaw to the right, and on the left pedal to make it yaw to the left. The rudder is used mainly to balance the aircraft in turns, or to compensate for winds or other effects that tend to turn the aircraft about the yaw axis.

• A throttle, which adjusts the thrust produced by the aircraft's engines. The pilot uses the throttle to increase or decrease the speed of the aircraft, and to adjust the aircraft's altitude (higher speeds cause the aircraft to climb, lower speeds cause it to descend). In some aircraft the throttle is a single lever that controls thrust; in others, adjusting the throttle means adjusting a number of different engine controls simultaneously. Aircraft with multiple engines usually have individual throttle controls for each engine.

• Brakes, used to slow and stop the aircraft on the ground, and sometimes for turns on the ground.

Other possible controls include:

• Flap levers, which are used to control the position of flaps on the wings. • Spoiler levers, which are used to control the position of spoilers on the wings, and

to arm their automatic deployment in aircraft designed to deploy them upon landing.

• Trim controls, which usually take the form of knobs or wheels and are used to adjust pitch, roll, or yaw trim. These are often connected to small airfoils on the trail edge of the control surfaces called 'trim tabs'.

• A tiller, a small wheel or lever used to steer the aircraft on the ground (in conjunction with or instead of the rudder pedals).

• A parking brake, used to prevent the aircraft from rolling when it is parked on the ground.

The controls may allow full or partial automation of flight, such as an autopilot, a wing leveler, or a flight management system. Pilots adjust these controls to select a specific attitude or mode of flight, and then the associated automation maintains that attitude or mode until the pilot disables the automation or changes the settings. In general, the larger and/or more complex the aircraft, the greater the amount of automation available to pilots.

On an aircraft with a pilot and copilot, or instructor and trainee, the aircraft is made capable of control without the crew changing seats. The most common arrangement is two complete sets of controls, one for each of two pilots sitting side by side, but in some aircraft (military fighter aircraft, some taildraggers and aerobatic aircraft) the dual sets of controls are arranged one in front of the other. A few of the less important controls may not be present in both positions, and one position is usually intended for the pilot in command (e.g., the left "captain's seat" in jet airliners). Some small aircraft use controls that can be moved from one position to another, such as a single yoke that can be swung into position in front of either the left-seat pilot or the right-seat pilot (i.e. Beechcraft Bonanza).

Aircraft that require more than one pilot usually have controls intended to suit each pilot position, but still with sufficient duplication so that all pilots can fly the aircraft alone in an emergency. For example, in jet airliners, the controls on the left (captain's) side include both the basic controls and those normally manipulated by the pilot in command, such as the tiller, whereas those of the right (first officer's) side include the basic controls again and those normally manipulated by the copilot, such as flap levers. The unduplicated controls that are required for flight are positioned so that they can be reached by either pilot, but they are often designed to be more convenient to the pilot who manipulates them under normal condition.

Instruments

Instruments provide information to the pilot and the co-pilot. Flight instruments provide information about the aircraft's speed, direction, altitude, and orientation. Powerplant instruments provide information about the status of the aircraft's Aircraft engine/engines and APU. Systems instruments provide information about the aircraft's other systems, such as fuel delivery, electrical, and pressurisation. Navigation and communication instruments include all the aircraft's radios. Instruments may operate mechanically or electrically, requiring 12VDC, 24VDC, or 400 Hz power systems. An aircraft that uses computerised CRT or LCD displays almost exclusively is said to have a glass cockpit.

Basic instruments include:

• An airspeed indicator, which indicates the speed at which the aircraft is moving through the surrounding air.

• An altimeter, which indicates the altitude of the aircraft above mean sea level. • A Heading indicator, (sometimes referred to as a "directional gyro (DG)") which

indicates the magnetic compass heading that the aircraft's fuselage is pointing

towards. The actual direction the aircraft is flying towards is affected by the wind conditions.

• An attitude indicator, sometimes called an artificial horizon, which indicates the exact orientation of the aircraft about its pitch and roll axes.

Other instruments might include:

• A Turn coordinator, which helps the pilot maintain the aircraft in a coordinated attitude while turning.

• A Vertical Speed Indicator, which shows the rate at which the aircraft is climbing or descending.

• A horizontal situation indicator, shows the position and movement of the aircraft as seen from above with respect to the ground, including course/heading and other information.

• Instruments showing the status of each engine in the aircraft (operating speed, thrust, temperature, and other variables).

• Combined display systems such as primary flight displays or navigation displays. • Information displays such as on-board weather radar displays.

Design and construction

The Blohm & Voss BV 141 had an unusually asymmetric design.

Most aircraft are constructed by companies with the objective of producing them in quantity for customers. The design and planning process, including safety tests, can last up to four years for small turboprops, and up to 12 years for aircraft with the capacity of the A380.

During this process, the objectives and design specifications of the aircraft are established. First the construction company uses drawings and equations, simulations, wind tunnel tests and experience to predict the behavior of the aircraft. Computers are used by companies to draw, plan and do initial simulations of the aircraft. Small models

and mockups of all or certain parts of the aircraft are then tested in wind tunnels to verify the aerodynamics of the aircraft.

When the design has passed through these processes, the company constructs a limited number of these aircraft for testing on the ground. Representatives from an aviation governing agency often make a first flight. The flight tests continue until the aircraft has fulfilled all the requirements. Then, the governing public agency of aviation of the country authorises the company to begin production of the aircraft.

In the United States, this agency is the Federal Aviation Administration (FAA), and in the European Union, Joint Aviation Authorities (JAA). In Canada, the public agency in charge and authorising the mass production of aircraft is Transport Canada.

In the case of the international sales of aircraft, a license from the public agency of aviation or transports of the country where the aircraft is also to be used is necessary. For example, aircraft from Airbus need to be certified by the FAA to be flown in the United States and vice versa, aircraft of Boeing need to be approved by the JAA to be flown in the European Union.

Quieter aircraft are becoming more and more needed due to the increase in air traffic, particularly over urban areas, as noise pollution is a major concern. MIT and Cambridge University have been designing delta-wing aircraft that are 25 times more silent (63 dB) than current craft and can be used for military and commercial purposes. The project is called the Silent Aircraft Initiative, but production models will not be available until around 2030.

Small aircraft can be designed and constructed by amateurs as homebuilts. Other homebuilt aircraft can be assembled using pre-manufactured kits of parts which can be assembled into a basic aircraft and must then be completed by the builder.

There are few companies that produce aircraft on a large scale. However, the production of an aircraft for one company is a process that actually involves dozens, or even hundreds, of other companies and plants, that produce the parts that go into the aircraft. For example, one company can be responsible for the production of the landing gear, while another one is responsible for the radar. The production of such parts is not limited to the same city or country; in the case of large aircraft manufacturing companies, such parts can come from all over the world.

The parts are sent to the main plant of the aircraft company, where the production line is located. In the case of large aircraft, production lines dedicated to the assembly of certain parts of the aircraft can exist, especially the wings and the fuselage.

When complete, an aircraft is rigorously inspected to search for imperfections and defects. After approval by inspectors, the aircraft is put through a series of flight tests to assure that all systems are working correctly and that the aircraft handles properly. Upon

passing these tests, the aircraft is ready to receive the "final touchups" (internal configuration, painting, etc.), and is then ready for the customer.

Safety There are three main statistics which may be used to compare the safety of various forms of travel:

Deaths per billion journeys Bus: 4.3 Rail: 20 Van: 20 Car: 40 Foot: 40 Water: 90 Air: 117 Bicycle: 170 Motorcycle: 1640

Deaths per billion hours Bus: 11.1 Rail: 30 Air: 30.8 Water: 50 Van: 60 Car: 130 Foot: 220 Bicycle: 550 Motorcycle: 4840

Deaths per billion kilometres Air: 0.05 Bus: 0.4 Rail: 0.6 Van: 1.2 Water: 2.6 Car: 3.1 Bicycle: 44.6 Foot: 54.2 Motorcycle: 108.9

It is worth noting that the air industry's insurers base their calculations on the "number of deaths per journey" statistic while the industry itself generally uses the "number of deaths per kilometre" statistic in press releases.

Environmental impact

Variants Fixed-wing aircraft can be sub-divided according to the means of propulsion they use.

Unpowered

Aircraft that primarily intended for unpowered flight include gliders (sometimes called sailplanes), hang gliders and paragliders. These are mainly used for recreation. After launch, further energy is obtained through the skillful exploitation of rising air in the atmosphere. Gliders that are used for the sport of gliding have high aerodynamic efficiency. The highest lift-to-drag ratio is 70:1, though 50:1 is more common. Glider flights of thousands of kilometres at average speeds over 200 km/h have been achieved. The glider is most commonly launched by a tow-plane or by a winch. Some gliders, called motor gliders, are equipped with engines (often retractable) and some are capable of self-launching. The most numerous unpowered aircraft are hang gliders and paragliders. These are foot-launched and are generally slower, smaller and less expensive than sailplanes. Hang gliders most often have flexible wings which are given shape by a frame, though some have rigid wings. This is in contrast to paragliders which have no frames in their wings. Military gliders have been used in war to deliver assault troops, and specialised gliders have been used in atmospheric and aerodynamic research. Experimental aircraft and winged spacecraft have also made unpowered landings.

Propeller

Aquila AT01

Smaller and older propeller aircraft make use of reciprocating internal combustion engines that turns a propeller to create thrust. They are quieter than jet aircraft, but they fly at lower speeds, and have lower load capacity compared to similar sized jet powered aircraft. However, they are significantly cheaper and much more economical than jets, and are generally the best option for people who need to transport a few passengers and/or small amounts of cargo. They are also the aircraft of choice for pilots who wish to own an aircraft.

Turboprop aircraft are a halfway point between propeller and jet: they use a turbine engine similar to a jet to turn propellers. These aircraft are popular with commuter and regional airlines, as they tend to be more economical on shorter journeys.

Jet

A Ukrainian An-225 Mriya is the world's largest fixed-wing aircraft

Jet aircraft make use of turbines for the creation of thrust. These engines are much more powerful than a reciprocating engine. As a consequence, they have greater weight capacity and fly faster than propeller driven aircraft. One drawback, however, is that they are noisy; this makes jet aircraft a source of noise pollution. However, turbofan jet engines are quieter, and they have seen widespread usage partly for that reason.

The jet aircraft was developed in Germany in 1931. The first jet was the Heinkel He 178, which was tested at Germany's Marienehe Airfield in 1939. In 1943 the Messerschmitt Me 262, the first jet fighter aircraft, went into service in the German Luftwaffe. In the early 1950s, only a few years after the first jet was produced in large numbers, the De Havilland Comet became the world's first jet airliner. However, the early Comets were beset by structural problems discovered after numerous pressurisation and depressurisation cycles, leading to extensive redesigns.

Most wide-body aircraft can carry hundreds of passengers and several tons of cargo, and are able to travel for distances up to 17,000 km. Aircraft in this category are the Boeing 747, Boeing 767, Boeing 777, Boeing 787 and Airbus A350, Airbus A300/A310, Airbus A330, Airbus A340, Airbus A380, Lockheed L-1011 TriStar, McDonnell Douglas DC-10, McDonnell Douglas MD-11, Ilyushin Il-86 and Ilyushin Il-96.

Jet aircraft possess high cruising speeds (700 to 900 km/h, or 400 to 550 mph) and high speeds for take-off and landing (150 to 250 km/h). Due to the speed needed for takeoff and landing, jet aircraft make use of flaps and leading edge devices for the control of lift and speed, as well as thrust reversers to direct the airflow forward, slowing down the aircraft upon landing.

Supersonic jet

Supersonic aircraft, such as military fighters and bombers, Concorde, and others, make use of turbines (often utilising afterburners), that generate the huge amounts of power for flight faster than the speed of the sound. Flight at supersonic speed creates more noise than flight at subsonic speeds, due to the phenomenon of sonic booms. This limits supersonic flights to areas of low population density or open ocean. When approaching an area of heavier population density, supersonic aircraft are obliged to fly at subsonic speed.

Due to the high costs, limited areas of use and low demand there are no longer any supersonic aircraft in use by any major airline. The last Concorde flight was on 26 November 2003.

Solar-powered

Helios in flight

A solar-powered aircraft generates the needed energy by means of solar cells. On 8 July 2010 the manned Solar Impulse became the first solar-powered aeroplane to fly through an entire night.

Unmanned

An aircraft is said to be 'unmanned' when there is no person aboard the aircraft and control is achieved remotely or via other means such as gyroscopes or other forms of autonomous control. The aircraft is controlled only by remote controls or other electronic devices.

Rocket-powered

Bell X-1A in flight

Experimental rocket powered aircraft were developed by the Germans as early as World War II, and about 29 were manufactured and deployed. The first fixed wing aircraft to break the sound barrier in level flight was a rocket plane – the Bell X-1. The later North American X-15 was another important rocket plane that broke many speed and altitude records and laid much of the groundwork for later aircraft and spacecraft design. Rocket aircraft are not in common usage today, although rocket-assisted takeoffs are used for some military aircraft. SpaceShipOne is a well known current rocket aircraft, it is the

prototype for development of a commercial sub-orbital passenger service. Another rocket plane is the XCOR EZ-Rocket.

Ramjet

USAF Lockheed SR-71 Blackbird trainer

A ramjet is a form of jet engine that contains no major moving parts and can be particularly useful in applications requiring a small and simple engine for high speed use, such as missiles. The D-21 Tagboard was an unmanned Mach 3+ reconnaissance drone that was put into production in 1969 for spying, but due to the development of better spy satellites, it was cancelled in 1971. The SR-71's Pratt & Whitney J58 engines ran 80% as ramjets at high speeds Mach 3.2. The SR-71 was dropped at the end of the Cold War, then brought back during the 1990s. They were used also in the Gulf War. The last SR-71 flight was in October 2001.

Scramjet

The Boeing X-43A, shortly after booster ignition

Scramjet aircraft are in the experimental stage. The Boeing X-43 is an experimental scramjet with a world speed record for a jet-powered aircraft – Mach 9.7, nearly 12,000 kilometres per hour (7,500 mph) at an altitude of about 36,000 metres (118,000 ft). The X-43A set the flight speed record on 16 November 2004.

4. Aeroelasticity Aeroelasticity is the science which studies the interactions among inertial, elastic, and aerodynamic forces. It was defined by Arthur Collar in 1947 as "the study of the mutual interaction that takes place within the triangle of the inertial, elastic, and aerodynamic forces acting on structural members exposed to an airstream, and the influence of this study on design."

Introduction Airplane structures are not completely rigid, and aeroelastic phenomena arise when structural deformations induce changes on aerodynamic forces. The additional aerodynamic forces cause an increase in the structural deformations, which leads to greater aerodynamic forces in a feedback process. These interactions may become smaller until a condition of equilibrium is reached, or may diverge catastrophically.

Aeroelasticity can be divided in two fields of study: steady (static) and dynamic aeroelasticity.

Steady aeroelasticity Steady aeroelasticity studies the interaction between aerodynamic and elastic forces on an elastic structure. Mass properties are not significant in the calculations of this type of phenomena.

Divergence

Divergence occurs when a lifting surface deflects under aerodynamic load so as to increase the applied load, or move the load so that the twisting effect on the structure is increased. The increased load deflects the structure further, which brings the structure to the limit loads and to failure.

Control surface reversal

Control surface reversal is the loss (or reversal) of the expected response of a control surface, due to structural deformation of the main lifting surface.

Dynamic aeroelasticity Dynamic Aeroelasticity studies the interactions among aerodynamic, elastic, and inertial forces. Examples of dynamic aeroelastic phenomena are:

Flutter

Flutter is a self-feeding and potentially destructive vibration where aerodynamic forces on an object couple with a structure's natural mode of vibration to produce rapid periodic motion. Flutter can occur in any object within a strong fluid flow, under the conditions that a positive feedback occurs between the structure's natural vibration and the aerodynamic forces. That is, that the vibrational movement of the object increases an aerodynamic load, which in turn drives the object to move further. If the energy during the period of aerodynamic excitation is larger than the natural damping of the system, the level of vibration will increase, resulting in self-exciting oscillation. The vibration levels can thus build up and are only limited when the aerodynamic or mechanical damping of the object match the energy input, which often results in large amplitudes and can lead to rapid failure. Because of this, structures exposed to aerodynamic forces - including wings, aerofoils, but also chimneys and bridges - are designed carefully within known parameters to avoid flutter. Flutter is not always a destructive force; recent progress has been made in small scale (table top) wind generators for underserved communities in developing countries, designed specifically to take advantage of this effect.

In complex structures where both the aerodynamics and the mechanical properties of the structure are not fully understood, flutter can only be discounted through detailed testing. Even changing the mass distribution of an aircraft or the stiffness of one component can induce flutter in an apparently unrelated aerodynamic component. At its mildest this can appear as a "buzz" in the aircraft structure, but at its most violent it can develop uncontrollably with great speed and cause serious damage to or the destruction of the aircraft.

In some cases, automatic control systems have been demonstrated to help prevent or limit flutter-related structural vibration.

Flutter can also occur on structures other than aircraft. One famous example of flutter phenomena is the collapse of the original Tacoma Narrows Bridge.

Dynamic response

Dynamic response or forced response is the response of an object to changes in a fluid flow such as aircraft to gusts and other external atmospheric disturbances. Forced response is a concern in axial compressor and gas turbine design, where one set of aerofoils pass through the wakes of the aerofoils upstream.

Buffeting

Buffeting is a high-frequency instability, caused by airflow separation or shock wave oscillations from one object striking another. It is caused by a sudden impulse of load increasing. It is a random forced vibration. Generally it affects the tail unit of the aircraft structure due to air flow down stream of the wing.

Other fields of study Other fields of physics may have an influence on aeroelastic phenomena. For example, in aerospace vehicles, stress induced by high temperatures is important. This leads to the study of aerothermoelasticity. Or, in other situations, the dynamics of the control system may affect aeroelastic phenomena. This is called aeroservoelasticity.

Prediction and cure Aeroelasticity involves not just the external aerodynamic loads and the way they change but also the structural, damping and mass characteristics of the aircraft. Prediction involves making a mathematical model of the aircraft as a series of masses connected by springs and dampers which are tuned to represent the dynamic characteristics of the aircraft structure. The model also includes details of applied aerodynamic forces and how they vary.

The model can be used to predict the flutter margin and, if necessary, test fixes to potential problems. Small carefully-chosen changes to mass distribution and local structural stiffness can be very effective in solving aeroelastic problems.

Media These videos detail the Active Aeroelastic Wing two-phase NASA-Air Force flight research program to investigate the potential of aerodynamically twisting flexible wings to improve maneuverability of high-performance aircraft at transonic and supersonic speeds, with traditional control surfaces such as ailerons and leading-edge flaps used to induce the twist.

Time lapsed film of Active Aeroelastic Wing (AAW) Wing loads test, December, 2002

F/A-18A (now X-53) Active Aeroelastic Wing (AAW) flight test, December, 2002

5. Flight test Flight test is a branch of aeronautical engineering that develops and gathers data during flight of an aircraft and then analyses the data to evaluate the flight characteristics of the aircraft and validate its design, including safety aspects. The flight test phase accomplishes two major tasks: 1) finding and fixing any aircraft design problems and then 2) verifying and documenting the aircraft capabilities for government certification or customer acceptance. The flight test phase can range from the test of a single new system for an existing aircraft to the complete development and certification of a new aircraft. Therefore the duration of a flight test program can vary from a few weeks to several years.

Civil Aircraft Flight Test There are typically two categories of flight test programs – commercial and military. Commercial flight testing is conducted to certify that the aircraft meets all applicable safety and performance requirements of the government certifying agency. In the US, this is the Federal Aviation Administration (FAA); in Canada, Transport Canada (TC); in the United Kingdom (UK), the Civil Aviation Authority; and in the European Union, the European Aviation Safety Agency (EASA). Since commercial aircraft development is normally funded by the aircraft manufacturer and/or private investors, the certifying agency does not have a stake in the commercial success of the aircraft. These civil agencies are concerned with the aircraft’s safety and that the pilot’s flight manual accurately reports the aircraft’s performance. The market will determine the aircraft’s suitability to operators. Normally, the civil certification agency does not get involved in flight testing until the manufacturer has found and fixed any development issues and is ready to seek certification.

Military aircraft Flight Test Military programs differ from commercial in that the government contracts with the aircraft manufacturer to design and build an aircraft to meet specific mission capabilities. These performance requirements are documented to the manufacturer in the Aircraft Specification and the details of the flight test program (among many other program requirements) are spelled out in the Statement of Work. In this case, the government is the customer and has a direct stake in the aircraft’s ability to perform the mission. Since the government is funding the program, it is more involved in the aircraft design and testing from early-on. Often military test pilots and engineers are integrated as part of the manufacturer’s flight test team, even before first flight. The final phase of the military aircraft flight test is the Operational Test (OT). OT is conducted by a government-only test team with the dictate to certify that the aircraft is suitable and effective to carry out the intended mission. Flight testing of military aircraft is often conducted at military flight test facilities. The US Navy tests aircraft at Naval Air Station Patuxent River, MD (a.k.a. “Pax River”) and the US Air Force at Edwards Air Force Base, CA. The U.S. Air Force Test Pilot School and the U.S. Naval Test Pilot School are the programs designed to teach military test personnel. In the UK most military flight testing is conducted by three organizations, the RAF, BAE Systems and QinetiQ. For minor upgrades the testing may be conducted by one of these three organisations in isolation, but major programs are normally conducted by a joint trials team (JTT), with all three organisations working together under the umbrella of an Integrated Project Team (IPT) airospace

Flight Test Processes Flight Testing is highly expensive and potentially very risky. Unforeseen problems can lead to damage to aircraft and loss of life, both of aircrew and people on the ground. For these reasons modern flight testing is probably one of the most safety conscious

professions today. Flight trials can be divided into 3 sections, planning, execution and analysis and reporting.

Preparation

For both commercial and military aircraft, flight test preparation begins well before the aircraft is ready to fly. Initially what needs to be tested must be defined, from which the Flight Test Engineers prepare the test plan, which is essentially certain manoeuvres to be flown (or systems to be exercised). A full certification/qualification flight test program for a new aircraft will require testing for many aircraft systems and in-flight regimes; each is typically documented in a separate test plan. During the actual flight testing, similar maneuvers from all test plans are combined and the data collected on the same flights, where practical. This allows the required data to be acquired in the minimum number of flight hours.

Once the flight test data requirements are established, the aircraft is instrumented to record that data for analysis. Typical instrumentation parameters recorded during a flight test are: temperatures, pressures, structural loads, vibration/accelerations, noise levels (interior and exterior), aircraft performance parameters (airspeed, altitude, etc.), aircraft controls positions (stick/yoke position, rudder pedal position, throttle position, etc.), engine performance parameters, and atmospheric conditions. During selected phases of flight test, especially during early development of a new aircraft, many parameters are transmitted to the ground during the flight and monitored by the Flight Test Engineer and test support engineers. This provides for safety monitoring and allows real-time analysis of the data being acquired.

Execution

When the aircraft is completely assembled and instrumented, it typically conducts many hours of ground testing before its first/maiden flight. This ground testing will verify basic aircraft systems operations, measure engine performance, evaluate dynamic systems stability, and provide a first look at structural loads. Flight controls will also be checked out. Once all required ground tests are completed, the aircraft is ready for the first flight. First/maiden flight is a major milestone in any aircraft development program and is undertaken with the utmost caution.

There are several aspects to a flight test program: handling qualities, performance, aero-elastic/flutter stability, avionics/systems capabilities, weapons delivery, and structural loads. Handling qualities evaluates the aircraft's controllability and response to pilot inputs throughout the range of flight. Performance testing evaluates aircraft in relation to its projected abilities, such as speed, range, power available, drag, airflow characteristics, and so forth. Aero-elastic stability evaluates the dynamic response of the aircraft controls and structure to aerodynamic (i.e. air-induced) loads. Structural tests measure the stresses on the airframe, dynamic components, and controls to verify structural integrity in all flight regimes. Avionics/systems testing verifies all electronic systems (navigation, communications, radars, sensors, etc.) perform as designed. Weapons delivery looks at

the pilot’s ability to acquire the target using on-board systems and accurately deliver the ordnance on target. Weapons delivery testing also evaluates the separation of the ordnance as it leaves the aircraft to ensure there are no safety issues. Other military unique tests are: air-to-air refueling, radar/infrared signature measurement, and aircraft carrier operations. Emergency situations are evaluated as a normal part of all flight test program. Examples are: engine failure during various phases of flight (takeoff, cruise, landing), systems failures, and controls degradation. The overall operations envelope (allowable gross weights, centers-of-gravity, altitude, max/min airspeeds, maneuvers, etc.) is established and verified during flight testing. Aircraft are always demonstrated to be safe beyond the limits allowed for normal operations in the Flight Manual.

Because the primary goal of a flight test program is to gather accurate engineering data, often on a design that is not fully proven, piloting a flight test aircraft requires a high degree of training and skill, so such programs are typically flown by a specially trained test pilot, and the data is gathered by a flight test engineer, and often visually displayed to the test pilot and/or flight test engineer using flight test instrumentation.

Analysis and Reporting

It includes the analysis of a flight for certification.It analyze the internal and outer part of the flight by checking its all minute parts. Reporting includes the analyzed data result.

Flight Test Team

The make-up of the Flight Test Team will vary with the organization and complexity of the flight test program, however, there are some key players who are generally part of all flight test organizations. The leader of a flight test team is usually a flight test engineer (FTE) or possibly an experimental [[test pilot]. Other FTEs or pilots could also be involved. Other team members would be the Flight Test Instrumentation Engineer, Instrumentation System Technicians, the aircraft maintenance department (mechanics, electricals, avionics technicians, etc.), Quality/Product Assurance Inspectors, the ground-based computing/data center personnel, plus logistics and administrative support. Engineers from various other disciplines would support the testing of their particular systems and analyze the data acquired for their specialty area.

Since many aircraft development programs are sponsored by government military services, military or government-employed civilian pilots and engineers are often integrated into the flight test team. The government representatives provide program oversight and review and approve data. Government test pilots may also participate in the actual test flights, possibly even on the first/maiden flight.

Chapter 4

Gravity Assist

In orbital mechanics and aerospace engineering, a gravitational slingshot, gravity assist maneuver or swing-by is the use of the relative movement and gravity of a planet or other celestial body to alter the path and speed of a spacecraft, typically in order to save propellant, time, and expense. Gravity assistance can be used to accelerate, decelerate and/or re-direct the path of a spacecraft. The "assist" is provided by the motion (orbital angular momentum) of the gravitating body as it pulls on the spacecraft. The technique was first proposed as a mid-course manoeuvre in 1961, and used by interplanetary probes from Mariner 10 onwards, including Voyagers' notable fly-bys of Jupiter and Saturn.

Explanation

Over-simplified example of gravitational slingshot: the spacecraft's velocity changes by up to twice the planet's velocity

A gravity assist or slingshot maneuver around a planet changes a spacecraft's velocity relative to the Sun, even though it preserves the spacecraft's speed relative to the planet—as it must according to the law of conservation of energy. To a first approximation, from a large distance, the spacecraft appears to have bounced off the planet. Physicists call this an elastic collision even though no actual contact occurs.

Suppose that you are a "stationary" observer and that you see: a planet moving left at speed U; a spaceship moving right at speed v. If the spaceship is on the right path, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction, to the left; and since the planet is moving left at speed U, the total velocity of the rocket relative

to you will be the velocity of the moving planet plus the velocity of the rocket with respect to the planet. So the velocity will be U + (U + v), that is 2U + v.

It might seem that this is oversimplified since the details of the orbit have not been covered, but it turns out that if the spaceship travels in a path which forms a hyperbola, it can leave the planet in the opposite direction without firing its engine, the speed gain at large distance is indeed 2U once it has left the gravity of the planet far behind.

This explanation might seem to violate the conservation of energy and momentum, but we have neglected the spacecraft's effects on the planet. The linear momentum gained by the spaceship is equal in magnitude to that lost by the planet, though the planet's enormous mass compared to the spacecraft makes the resulting change in its speed negligibly small. These effects on the planet are so slight (because planets are so much more massive than spacecraft) that they can be ignored in the calculation.

Realistic portrayals of encounters in space require the consideration of three dimensions. The same principles apply, only adding the planet's velocity to that of the spacecraft requires vector addition, as shown below.

2 dimensional schematic of gravitational slingshot. The arrows show the direction in which the spacecraft is traveling before and after the encounter. The arrows' length shows the spacecraft's speed.

Due to the reversibility of orbits gravitational slingshots can also be used to decelerate a spacecraft. Mariner 10 did it in 1974 and MESSENGER is also doing it, both to reach Mercury.

If even more speed is needed than available from gravity assist alone, the most economical way to utilize a rocket burn is to do it near the periapsis (closest approach). A given rocket burn always provides the same change in velocity (Δv), but the change in kinetic energy is proportional to the vehicle's velocity at the time of the burn. So to get the most kinetic energy from the burn, the burn must occur at the vehicle's maximum velocity, at periapsis. Powered slingshots describes this technique in more detail.

Historical origins of the method In his paper “Тем кто будет читать, чтобы строить” (To whoever will read [this paper] in order to build [an interplanetary rocket]), which he dated “1918-1919,” Yuri Kondratyuk suggested that a spacecraft traveling between two planets could be accelerated at the beginning of its trajectory and decelerated at the end of its trajectory by using the gravity of the two planets' moons.

In his 1925 paper “Проблема полета при помощи реактивных аппаратов: межпланетные полеты” [Problems of flight by jet propulsion: interplanetary flights], Friedrich Zander made a similar argument.

However, neither investigator realized that gravitational assists from planets along a spacecraft’s trajectory could propel a spacecraft and that therefore such assists could greatly reduce the amount of propellant required to travel among the planets. That discovery was made by Michael Minovitch in 1961.

The gravity assist maneuver was first used in 1959 when the Soviet probe Luna 3 photographed the far side of Earth's Moon. The maneuver relied on research performed at the Department of Applied Mathematics of Steklov Institute.

Why gravitational slingshots are used A spacecraft traveling to an inner planet will accelerate because it is falling toward the Sun, and a spacecraft traveling to an outer planet will decelerate because it is leaving the vicinity of the Sun.

Although it is true that the orbital speed of an inner planet is greater than that of the Earth, a spacecraft traveling to an inner planet, even at the minimum speed needed to reach it, is still accelerated by the Sun's gravity to a speed notably greater than the orbital speed of that destination planet. If the spacecraft's purpose is only to fly by the inner planet, then there is typically no need to slow the spacecraft. However, if the spacecraft is to be inserted into orbit about that inner planet, then there must be some way to slow the spacecraft.

Similarly, while the orbital speed of an outer planet is less than that of the Earth, a spacecraft leaving the Earth at the minimum speed needed to travel to some outer planet is decelerated by the Sun's gravity to a speed far less than the orbital speed of that outer planet. Thus, there must be some way to accelerate the spacecraft when it reaches that outer planet if it is to enter orbit about it. However, if the spacecraft is accelerated to more than the minimum required, less total propellant will be needed to enter orbit about the target planet. Also, accelerating the spacecraft early in the flight will, of course, reduce the travel time.

Rocket engines can certainly be used to accelerate and decelerate the spacecraft. However, rocket thrust takes propellant, propellant has mass, and even a small added delta-v requirement translates to far larger amounts of propellant needed to escape Earth's gravity well. This is because not only must the primary stage engines lift that extra propellant, they must also lift more propellant still, to lift that additional propellant. Thus the liftoff mass requirement increases exponentially with an increase in the required delta-V of the spacecraft.

Since a gravity assist maneuver can change the speed of a spacecraft without expending propellant, if and when possible, combined with aerobraking, can save significant amounts of propellant.

As an example, the MESSENGER mission is using gravity assist maneuvering to slow the spacecraft on its way to Mercury; however, since Mercury has almost no atmosphere, aerobraking cannot be used for insertion into orbit about it.

Journeys to the nearest planets, Mars and Venus, use a Hohmann transfer orbit, an elliptical path which starts as a tangent to one planet's orbit round the Sun and finishes as a tangent to the other. This method uses very nearly the smallest possible amount of fuel, but is very slow — it can take over a year to travel from Earth to Mars (fuzzy orbits use even less fuel, but are even slower).

Similarly it might take decades for a spaceship to travel to the outer planets (Jupiter, Saturn, Uranus, etc.) using a Hohmann transfer orbit, and it would still require far too much propellant, because the spacecraft would have to travel for 500 million miles (800 million km) or more against the force of the Sun's gravity. As gravitational assist maneuvers offer the only way to gain speed without using propellant, all missions to the outer planets have used it.

Limits to slingshot use The main practical limit to the use of a Gravity assist maneuver is that planets and other large masses are seldom in the right places to enable a voyage to a particular destination. For example the Voyager missions which started in the late 1970s were made possible by the "Grand Tour" alignment of Jupiter, Saturn, Uranus and Neptune. A similar alignment will not occur again until the middle of the 22nd century. That is an extreme case, but

even for less ambitious missions there are years when the planets are scattered in unsuitable parts of their orbits.

Another limitation is the atmosphere, if any, of the available planet. The closer the spacecraft can approach, the more boost it gets, because gravity falls off with the square of distance from a planet's center. If a spacecraft gets too far into the atmosphere, the energy lost to friction can exceed that gained from the planet's gravity. On the other hand, the atmosphere can be used to accomplish aerobraking. There have also been (so far theoretical) proposals to use aerodynamic lift as the spacecraft flies through the atmosphere (an aerogravity assist). This could bend the trajectory through a larger angle than gravity alone, and hence increase the gain in energy.

Interplanetary slingshots using the Sun itself are not possible because the Sun is at rest relative to the Solar System as a whole. However, thrusting when near the Sun has the same effect as the powered slingshot described below. This has the potential to magnify a spacecraft's thrusting power enormously, but is limited by the spacecraft's ability to resist the heat.

An interstellar slingshot using the Sun is conceivable, involving for example an object coming from elsewhere in our galaxy and swinging past the Sun to boost its galactic travel. The energy and angular momentum would then come from the Sun's orbit around the Milky Way.

Another theoretical limit is based on general relativity. If a spacecraft gets close to the Schwarzschild radius of a black hole (the ultimate gravity well), space becomes so curved that slingshot orbits require more energy to escape than the energy that could be added by the black hole's motion.

A rotating black hole might provide additional assistance, if its spin axis is aligned the right way. General relativity predicts that a large spinning mass produces frame-dragging — close to the object, space itself is dragged around in the direction of the spin. In theory an ordinary star produces this effect, although attempts to measure frame dragging about the Sun have produced no clear evidence. Experiments performed by Gravity Probe B looking for frame-dragging effects caused by the Earth have not revealed clear evidence either. General relativity predicts that a spinning black hole is surrounded by a region of space, called the ergosphere, within which standing still (with respect to the black hole's spin) is impossible, because space itself is dragged at the speed of light in the same direction as the black hole's spin. The Penrose process may offer a way to gain energy from the ergosphere, although it would require the spaceship to dump some "ballast" into the black hole, and the spaceship would have had to expend energy to carry the "ballast" to the black hole.

Timeline of notable examples

Mariner 10 – first use

The Mariner 10 probe was the first spacecraft to use the gravitational slingshot effect to reach another planet, passing by Venus on February 5, 1974, on its way to becoming the first spacecraft to explore Mercury.

Voyager 1 – furthest human-made object

As of January 21, 2010, Voyager 1 is over 16.81 terameters (1.681 × 1013 meters, or 1.681 × 1010 km, 112.4 AU, or 10.4 billion miles) from the Sun, and is in the boundary zone between the Solar System and interstellar space. It gained the energy to escape the Sun's gravity completely by performing slingshot maneuvers around Jupiter and Saturn.

Galileo – a change of plan

The Galileo spacecraft was launched by NASA in 1989 aboard Space Shuttle Atlantis. Its original mission was designed to use a direct Hohmann transfer. However, Galileo's intended booster, the cryogenically fueled (Hydrogen/Oxygen) Centaur booster rocket was prohibited as a Shuttle "cargo" for safety considerations following the loss of the Space Shuttle Challenger. Forced to substitute a lower delta V capable solid rocket upperstage, the IUS, instead of ascending directly to Jupiter, Galileo flew by Venus once and Earth twice in order to reach Jupiter in December, 1995.

The Galileo engineering review speculated (but was never able to prove conclusively) that this longer flight time coupled with the stronger sunlight near Venus caused lubricant in Galileo's main antenna to fail, forcing the use of a much smaller backup antenna with a consequent lowering of data rate from the spacecraft.

Its subsequent tour of the Jovian moons also used numerous slingshot maneuvers with those moons to conserve fuel and maximize the number of encounters.

The Ulysses probe changed the plane of its trajectory

In 1990, NASA launched the ESA spacecraft Ulysses to study the polar regions of the Sun. All the planets orbit approximately in a plane aligned with the equator of the Sun. Thus, to enter an orbit passing over the poles of the Sun, the spacecraft would have to eliminate the 30 km/s speed it inherited from the Earth's orbit around the Sun and gain the speed needed to orbit the Sun in the pole-to-pole plane — tasks that are impossible with current spacecraft propulsion systems alone, making gravity assist maneuvers essential.

Accordingly, Ulysses was first sent towards Jupiter, aimed to arrive at a point in space just "in front of" and "below" the planet. As it passed Jupiter, the probe 'fell' through the

planet's gravity field, exchanging momentum with the planet; this gravity assist maneuver bent the probe's trajectory up out of the planetary plane into an orbit that passed over the poles of the Sun. By using this maneuver, Ulysses needed only enough propellant to send it to a point near Jupiter, which is well within current capability.

MESSENGER

The MESSENGER mission is making extensive use of gravity assists to slow its speed before orbiting Mercury. The MESSENGER mission includes one flyby of Earth, two flybys of Venus, and three flybys of Mercury before finally arriving at Mercury in March 2011 with a velocity low enough to permit orbit insertion with the available fuel. Although the flybys are primarily orbital maneuvers, each provides an opportunity for significant scientific observations.

The Cassini probe – multiple gravity assists

The Cassini probe passed by Venus twice, then Earth, and finally Jupiter on the way to Saturn. The 6.7-year transit was slightly longer than the six years needed for a Hohmann transfer, but cut the total amount of delta V needed to about 2 km/s, so that the large and heavy Cassini probe was able to reach Saturn even with the small boosters available. A Hohmann transfer to Saturn would require a total of 15.7 km/s delta V (disregarding Earth's and Saturn's own gravity wells, and disregarding aerobraking), which is not within the capabilities of current spacecraft boosters.

Cassini's speed related to Sun. The various gravity assists form visible peaks on the left, while the periodic variation on the right is caused by the spacecraft's orbit around Saturn. The data was from JPL Horizons Ephemeris System. The speed above is in kilometers per second. Note also that the minimum speed achieved during Saturnian orbit is more or less equal to Saturn's own orbital velocity, which is the ~5 km/s velocity which Cassini matched to enter orbit.

Solar Probe+

The NASA Solar Probe+ mission, scheduled for launch in 2015, uses multiple gravity assists at Venus to remove the Earth's angular momentum from the orbit, in order to drop down to a distance of 9.5 solar radii from the sun. This will be the closest approach to the sun of any space mission.

Powered slingshots A well-established way to get more energy from a gravity assist is to fire a rocket engine at periapsis where a spacecraft is at its maximum velocity.

Rocket engines produce the same acceleration regardless of their initial velocity. A rocket acting on a fixed object, as in a static firing, does no useful work at all; the rocket's stored energy is entirely expended on its propellant. But when the rocket and its payload are free to move, the force applied by the rocket during any time interval acts through the distance the rocket and payload move during that time. Force acting through a distance is the definition of mechanical energy or work. So the farther the rocket and payload move during any given interval, i.e., the faster they move, the greater the kinetic energy imparted to the payload by the rocket. (This is why rockets are seldom used on slow-moving vehicles; they're simply too inefficient when used in that manner.)

Energy is still conserved, however. The additional energy imparted to the payload is exactly matched by a decrease in energy imparted to the propellant being expelled behind the rocket. This is because the velocity of the rocket is being subtracted from the propellant exhaust velocity. But we don't care about what happens to the propellant, so the faster we can move the rocket during a burn, the better.

To impart the most kinetic energy to a spacecraft whose free-fall velocity varies with time, we must do it when it's moving the fastest. As this occurs at periapsis, the closest approach to the planet, that's when we do the burn.

Another way to look at this is to note that by bringing in propellant as we fall into the planet's gravity well and leaving it behind there, we are able to extract much of the gravitational potential energy that was contained in that propellant.

There are also proposals to use aerodynamic lift at the point of closest approach (an aerogravity assist), to achieve a larger deflection and hence more energy gain.

Chapter 5

Introduction to Aerodynamics

A vortex is created by the passage of an aircraft wing, revealed by smoke. Vortices are one of the many phenomena associated to the study of aerodynamics. The equations of aerodynamics show that the vortex is created by the difference in pressure between the upper and lower surface of the wing. At the end of the wing, the lower surface effectively tries to 'reach over' to the low pressure side, creating rotation and the vortex.

Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with the difference being that gas dynamics applies to all gases. Understanding the motion of air (often called a flow field) around an object enables the calculation of forces and moments acting on the object. Typical properties calculated for a flow field include velocity, pressure, density and temperature as a function of position and time. By defining a control volume around the flow field, equations for the conservation of mass, momentum, and energy can be defined and used to solve for the properties. The use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations form the scientific basis for heavier-than-air flight.

Aerodynamic problems can be identified in a number of ways. The flow environment defines the first classification criterion. External aerodynamics is the study of flow around solid objects of various shapes. Evaluating the lift and drag on an airplane or the shock waves that form in front of the nose of a rocket are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine or through an air conditioning pipe.

The ratio of the problem's characteristic flow speed to the speed of sound comprises a second classification of aerodynamic problems. A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present (normally when the characteristic speed is approximately the speed of sound), supersonic when the characteristic flow speed is greater than the speed of sound, and hypersonic when the flow speed is much greater than the speed of sound. Aerodynamicists disagree over the precise definition of hypersonic flow; minimum Mach numbers for hypersonic flow range from 3 to 12.

The influence of viscosity in the flow dictates a third classification. Some problems may encounter only very small viscous effects on the solution, in which case viscosity can be considered to be negligible. The approximations to these problems are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

History

Early ideas - ancient times to the 17th century

A drawing of a design for a flying machine by Leonardo da Vinci (c. 1488). This machine was an ornithopter, with flapping wings similar to a bird, first presented in his Codex on the Flight of Birds in 1505.

Images and stories of flight have appeared throughout recorded history, such as the legendary story of Icarus and Daedalus, and the glider flight of Abbas Ibn Firnas. Although observations of some aerodynamic effects like wind resistance (a.k.a. drag) were recorded by the likes of Aristotle, Leonardo da Vinci and Galileo Galilei, very little effort was made to develop governing laws for understanding the nature of flight prior to the 17th century.

In 1505, Leonardo da Vinci wrote the Codex on the Flight of Birds, one of the earliest treatises on aerodynamics. He notes for the first time that the center of gravity of a flying bird does not coincide with its center of pressure, and he describes the construction of an ornithopter, with flapping wings similar to a bird's.

Sir Isaac Newton was the first person to develop a theory of air resistance, making him one of the first aerodynamicists. As part of that theory, Newton believed that drag was

due to the dimensions of a body, the density of the fluid, and the velocity raised to the second power. These beliefs all turned out to be correct for low flow speeds. Newton also developed a law for the drag force on a flat plate inclined towards the direction of the fluid flow. Using F for the drag force, ρ for the density, S for the area of the flat plate, V for the flow velocity, and θ for the inclination angle, his law was expressed as F = ρSV2sin2(θ)

Unfortunately, this equation is completely incorrect for the calculation of drag (unless the flow speed is hypersonic). Drag on a flat plate is closer to being linear with the angle of inclination as opposed to acting quadratically. This formula can lead one to believe that flight is more difficult than it actually is, and it may have contributed to a delay in human flight.

Modern beginnings - 18th to 19th century

A drawing of a glider by Sir George Cayley, one of the early attempts at creating an aerodynamic shape.

In 1738 The Dutch-Swiss mathematician Daniel Bernoulli published his book Hydrodynamica, in which he first set out the principle, named after him, by which aerodynamic lift may be derived.

Sir George Cayley is credited as the first person to identify the four aerodynamic forces of flight—weight, lift, drag, and thrust—and the relationship between them. Cayley believed that the drag on a flying machine must be counteracted by a means of propulsion in order for level flight to occur. Cayley also looked to nature for aerodynamic shapes with low drag. Among the shapes he investigated were the cross-sections of trout. This may appear counterintuitive, however, the bodies of fish are shaped to produce very low resistance as they travel through water. Their cross-sections are sometimes very close to that of modern low drag airfoils.

Air resistance experiments were carried out by investigators throughout the 18th and 19th centuries. Drag theories were developed by Jean le Rond d'Alembert, Gustav Kirchhoff, and Lord Rayleigh. Equations for fluid flow with friction were developed by Claude-Louis Navier and George Gabriel Stokes. To simulate fluid flow, many experiments involved immersing objects in streams of water or simply dropping them off the top of a tall building. Towards the end of this time period Gustave Eiffel used his Eiffel Tower to assist in the drop testing of flat plates.

Of course, a more precise way to measure resistance is to place an object within an artificial, uniform stream of air where the velocity is known. The first person to experiment in this fashion was Francis Herbert Wenham, who in doing so constructed the first wind tunnel in 1871. Wenham was also a member of the first professional organization dedicated to aeronautics, the Royal Aeronautical Society of the United Kingdom. Objects placed in wind tunnel models are almost always smaller than in practice, so a method was needed to relate small scale models to their real-life counterparts. This was achieved with the invention of the dimensionless Reynolds number by Osborne Reynolds. Reynolds also experimented with laminar to turbulent flow transition in 1883.

By the late 19th century, two problems were identified before heavier-than-air flight could be realized. The first was the creation of low-drag, high-lift aerodynamic wings. The second problem was how to determine the power needed for sustained flight. During this time, the groundwork was laid down for modern day fluid dynamics and aerodynamics, with other less scientifically inclined enthusiasts testing various flying machines with little success.

A replica of the Wright Brothers' wind tunnel is on display at the Virginia Air and Space Center. Wind tunnels were key in the development and validation of the laws of aerodynamics.

In 1889, Charles Renard, a French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight. Renard and German physicist Hermann von Helmholtz explored the wing loading of birds, eventually concluding that humans could not fly under their own power by attaching wings onto their arms. Otto Lilienthal, following the work of Sir George Cayley, was the first person to become highly successful with glider flights. Lilienthal believed that thin, curved airfoils would produce high lift and low drag.

Octave Chanute provided a great service to those interested in aerodynamics and flying machines by publishing a book outlining all of the research conducted around the world up to 1893.

Practical flight - early 20th century

With the information contained in Chanute's book, the personal assistance of Chanute himself, and research carried out in their own wind tunnel, the Wright brothers gained just enough knowledge of aerodynamics to fly the first powered aircraft on December 17, 1903, just in time to beat the efforts of Samuel Pierpont Langley. The Wright brothers'

flight confirmed or disproved a number of aerodynamics theories. Newton's drag force theory was finally proved incorrect. This first widely-publicised flight led to a more organized effort between aviators and scientists, leading the way to modern aerodynamics.

During the time of the first flights, Frederick W. Lanchester, Martin Wilhelm Kutta, and Nikolai Zhukovsky independently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two-dimensional wing theory. Expanding upon the work of Lanchester, Ludwig Prandtl is credited with developing the mathematics behind thin-airfoil and lifting-line theories as well as work with boundary layers. Prandtl, a professor at the University of Göttingen, instructed many students who would play important roles in the development of aerodynamics like Theodore von Kármán and Max Munk.

Faster than sound - latter 20th century

As aircraft began to travel faster, aerodynamicists realized that the density of air began to change as it came into contact with an object, leading to a division of fluid flow into the incompressible and compressible regimes. In compressible aerodynamics, density and pressure both change, which is the basis for calculating the speed of sound. Newton was the first to develop a mathematical model for calculating the speed of sound, but it was not correct until Pierre-Simon Laplace accounted for the molecular behavior of gases and introduced the heat capacity ratio. The ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach, who was one of the first to investigate the properties of supersonic flow which included Schlieren photography techniques to visualize the changes in density. William John Macquorn Rankine and Pierre Henri Hugoniot independently developed the theory for flow properties before and after a shock wave. Jakob Ackeret led the initial work on calculating the lift and drag on a supersonic airfoil. Theodore von Kármán and Hugh Latimer Dryden introduced the term transonic to describe flow speeds around Mach 1 where drag increases rapidly. Because of the increase in drag approaching Mach 1, aerodynamicists and aviators disagreed on whether supersonic flight was achievable.

A computer generated model of NASA's X-43A hypersonic research vehicle flying at Mach 7 using a computational fluid dynamics code.

On September 30, 1935 an exclusive conference was held in Rome with the topic of high velocity flight and the possibility of breaking the sound barrier. Participants included Theodore von Kármán, Ludwig Prandtl, Jakob Ackeret, Eastman Jacobs, Adolf Busemann, Geoffrey Ingram Taylor, Gaetano Arturo Crocco, and Enrico Pistolesi. The new research presented was impressive. Ackeret presented a design for a supersonic wind tunnel. Busemann gave perhaps the best presentation on the need for aircraft with swept wings for high speed flight. Eastman Jacobs, working for NACA, presented his optimized airfoils for high subsonic speeds which led to some of the high performance American aircraft during World War II. Supersonic propulsion was also discussed. The sound barrier was broken using the Bell X-1 aircraft twelve years later, thanks in part to those individuals.

By the time the sound barrier was broken, much of the subsonic and low supersonic aerodynamics knowledge had matured. The Cold War fueled an ever evolving line of high performance aircraft. Computational fluid dynamics was started as an effort to solve for flow properties around complex objects and has rapidly grown to the point where entire aircraft can be designed using a computer.

With some exceptions, the knowledge of hypersonic aerodynamics has matured between the 1960s and the present decade. Therefore, the goals of an aerodynamicist have shifted from understanding the behavior of fluid flow to understanding how to engineer a vehicle to interact appropriately with the fluid flow. For example, while the behavior of

hypersonic flow is understood, building a scramjet aircraft to fly at hypersonic speeds has seen very limited success. Along with building a successful scramjet aircraft, the desire to improve the aerodynamic efficiency of current aircraft and propulsion systems will continue to fuel new research in aerodynamics.

Continuity assumption Gases are composed of molecules which collide with one another and solid objects. If density and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another, the discrete molecular nature of a gas is ignored.

The continuity assumption becomes less valid as a gas becomes more rarefied. In these cases, statistical mechanics is a more valid method of solving the problem than continuous aerodynamics. The Knudsen number can be used to guide the choice between statistical mechanics and the continuous formulation of aerodynamics.

Laws of conservation

Control volume schematic of internal flow with one inlet and exit including an axial force, work, and heat transfer. State 1 is the inlet and state 2 is the exit.

Aerodynamics problems are often solved using conservation laws as applied to a fluid continuum. The conservation laws can be written in integral or differential form. In many basic problems, three conservation principles are used:

• Continuity: If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume. In fluid dynamics, the continuity equation is analogous to Kirchhoff's Current Law in electric circuits. The differential form of the continuity equation is:

Above, ρ is the fluid density, u is a velocity vector, and t is time. Physically, the equation also shows that mass is neither created nor destroyed in the control volume. For a steady state process, the rate at which mass enters the volume is equal to the rate at which it leaves the volume. Consequently, the first term on the left is then equal to zero. For flow through a tube with one inlet (state 1) and exit (state 2) as shown in the figure in this section, the continuity equation may be written and solved as:

Above, A is the variable cross-section area of the tube at the inlet and exit. For incompressible flows, density remains constant.

• Conservation of Momentum: This equation applies Newton's second law of motion to a continuum, whereby force is equal to the time derivative of momentum. Both surface and body forces are accounted for in this equation. For instance, F could be expanded into an expression for the frictional force acting on an internal flow.

For the same figure, a control volume analysis yields:

Above, the force F is placed on the left side of the equation, assuming it acts with the flow moving in a left-to-right direction. Depending on the other properties of the flow, the resulting force could be negative which means it acts in the opposite direction as depicted in the figure.

• Conservation of Energy: Although energy can be converted from one form to another, the total energy in a given system remains constant.

Above, h is enthalpy, k is the thermal conductivity of the fluid, T is temperature, and Φ is the viscous dissipation function. The viscous dissipation function governs the rate at which mechanical energy of the flow is converted to heat. The expression on the left side is a material derivative. The term is always positive since, according to the second law of thermodynamics, viscosity cannot add energy to the control volume. Again using the figure, the energy equation in terms of the control volume may be written as:

Above, the shaft work and heat transfer are assumed to be acting on the flow. They may be positive (to the flow from the surroundings) or negative (to the surroundings form the flow) depending on the problem. The ideal gas law or another equation of state is often used in conjunction with these equations to form a system to solve for the unknown variables.

Subsonic flow

Subsonic (or low-speed) aerodynamics is the study of fluid motion which is everywhere much slower than the speed of sound through the fluid or gas. There are several branches of subsonic flow but one special case arises when the flow is inviscid, incompressible and irrotational. This case is called Potential flow and allows the differential equations used to be a simplified version of the governing equations of fluid dynamics, thus making available to the aerodynamicist a range of quick and easy solutions. It is a special case of Subsonic aerodynamics.

In solving a subsonic problem, one decision to be made by the aerodynamicist is whether to incorporate the effects of compressibility. Compressibility is a description of the amount of change of density in the problem. When the effects of compressibility on the solution are small, the aerodynamicist may choose to assume that density is constant. The problem is then an incompressible low-speed aerodynamics problem. When the density is allowed to vary, the problem is called a compressible problem. In air, compressibility effects are usually ignored when the Mach number in the flow does not exceed 0.3 (about 335 feet (102m) per second or 228 miles (366 km) per hour at 60oF). Above 0.3, the problem should be solved by using compressible aerodynamics.

Associated terminology The incompressible and compressible flow regimes produce many associated phenomena, such as boundary layers and turbulence.

Chapter 6

Lift (force) and Drag

Lift (force)

Airbus A380 taking off during the Paris Air Show in 2007.

A fluid flowing past the surface of a body exerts a surface force on it. Lift is defined to be the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is defined to be the component of the surface force parallel to the flow direction.

Overview

Forces on an airfoil.

If the fluid is air, the force is called an aerodynamic force. An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. Aerodynamic lift is commonly associated with the wing of a fixed-wing aircraft, although lift is also generated by propellers; kites; helicopter rotors; rudders, sails and keels on sailboats; hydrofoils; wings on auto racing cars; wind turbines and other streamlined objects. While common meanings of the word "lift" suggest that lift opposes gravity, lift can be in any direction. When an aircraft is flying straight and level (cruise) most of the lift opposes gravity. However, when an aircraft is climbing, descending, or banking in a turn, for example, the lift is tilted with respect to the vertical. Lift may also be entirely downwards in some aerobatic manoeuvres, or on the wing on a racing car. In this last case, the term downforce is often used. Lift may also be horizontal, for instance on a sail on a sailboat.

Non-streamlined objects such as bluff bodies and plates (not parallel to the flow) may also generate lift when moving relative to the fluid. This lift may be steady, or it may oscillate due to vortex shedding. Interaction of the object's flexibility with the vortex shedding may enhance the effects of fluctuating lift and cause vortex-induced vibrations.

Description of lift on an airfoil There are several ways to explain how an airfoil generates lift. Some are more complicated or more mathematically rigorous than others; some have been shown to be incorrect.

Newton's laws: Lift and the deflection of the flow

Deflection

Airstreams around an airfoil in a wind tunnel. Note the curved streamlines and the overall downward deflection of the air.

One way to understand the generation of lift is to observe that the air is deflected as it passes the airfoil. Since the airfoil must exert a force on the air to change its direction, the air must exert an equal but opposite force on the airfoil. In the case of an airplane wing, the wing exerts a downward force on the air and the air exerts an upward force on the wing. This explanation relies on the second and third of Newton's laws of motion: The net force on an object is equal to its rate of momentum change, and: To every action there is an equal and opposite reaction.

Flow turning

Another way to describe deflection is to say that the air "turns" as it passes the airfoil and follows a path that is curved. When airflow changes direction, a force is generated.

Pressure differences

It may also be described in terms of air pressure: pressure is just force per unit area perpendicular to that area. So, wherever there is force there is also a pressure difference. Since deflection/flow turning tells us that there is a force, it also tells us there is a pressure difference. This pressure difference implies higher pressure on the underside of the wing and lower pressure on the upper side.

Criticisms of deflection/turning

• While the theory correctly reasons that deflection implies that there must be a force on the wing, it does not explain why the air is deflected. Intuitively, one can say that the air follows the curve of the foil, but this is not very rigorous or precise.

• The theory, while correct in as far as it goes, is not sufficient to allow one to do engineering. Fluid stresses – including pressure – need to be related to the fluid motion (e.g. through constitutive equations). Thus, textbooks on aerodynamics use more complex models to provide a full description of lift.

A more rigorous physical description

Flow around an airfoil: the dots move with the flow. Note that the velocities are much higher at the upper surface than at the lower surface. The black dots are on timelines, which split into two — an upper and lower part — at the leading edge. The part of a timeline below the airfoil does not catch up with the one above. Colors of the dots indicate streamlines. The airfoil is a Kármán–Trefftz airfoil, with parameters μx = –0.08, μy = +0.08 and n = 1.94. The angle of attack is 8°, and the flow is a potential flow.

Lift is generated in accordance with the fundamental principles of physics. The most relevant physics reduce to three principles:

• Newton's laws of motion, especially Newton's second law which relates the net force on an element of air to its rate of momentum change,

• conservation of mass, including the common assumption that the airfoil's surface is impermeable for the air flowing around, and

• an expression relating the fluid stresses (consisting of pressure and shear stress components) to the properties of the flow.

In the last principle, the pressure depends on the other flow properties, such as its mass density, through the (thermodynamic) equation of state, while the shear stresses are related to the flow through the air's viscosity. Application of the viscous shear stresses to Newton's second law for an airflow results in the Navier–Stokes equations. But in many instances approximations suffice for a good description of lifting airfoils: in large parts of the flow viscosity may be neglected. Such an inviscid flow can be described mathematically through the Euler equations, resulting from the Navier-Stokes equations when the viscosity is neglected.

The Euler equations for a steady and inviscid flow can be integrated along a streamline, resulting in Bernoulli's equation. The particular form of Bernoulli's equation found depends on the equation of state used. At low Mach numbers, compressibility effects may be neglected, resulting in an incompressible flow approximation. In incompressible and inviscid flow the Bernoulli equation is just an integration of Newton's second law—in the form of the description of momentum evolution by the Euler equations—along a streamline.

Explaining lift while considering all of the principles involved is a complex task and is not easily simplified. As a result, there are numerous different explanations of lift with different levels of rigour and complexity. For example, there is an explanation based directly on Newton’s laws of motion; and an explanation based on Bernoulli’s principle. Neither of these explanations is incorrect, but each appeals to a different audience.

In order to explain lift as it applies to an airplane wing, consider the incompressible flow around a 2-D, symmetric airfoil at positive angle of attack in a uniform freestream. Instead of considering the case where an airfoil moves through a fluid as seen by a stationary observer, it is equivalent and simpler to consider the picture when the observer follows the airfoil and the fluid moves past it.

Lift in an established flow

Streamlines around a NACA 0012 airfoil at moderate angle of attack.

If one takes the experimentally observed flow around an airfoil as a starting point, then lift can be explained in terms of pressures using Bernoulli's principle (which can be derived from Newton's second law) and conservation of mass.

The image to the right shows the streamlines over a NACA 0012 airfoil computed using potential flow theory, a simplified model of the real flow. The flow approaching an airfoil can be divided into two streamtubes, which are defined based on the area between two streamlines. By definition, fluid never crosses a streamline in a steady flow; hence mass is conserved within each streamtube. One streamtube travels over the upper surface, while the other travels over the lower surface; dividing these two tubes is a dividing line (the stagnation streamline) that intersects the airfoil on the lower surface, typically near to the leading edge. The stagnation streamline leaves the airfoil at the sharp trailing edge, a feature of the flow known as the Kutta condition. In calculating the flow shown, the Kutta condition was imposed as an initial assumption; the justification for this assumption is explained below.

The upper stream tube constricts as it flows up and around the airfoil, a part of the so-called upwash. From the conservation of mass, the flow speed must increase as the stream tube area decreases. The area of the lower stream tube increases, causing the flow

inside the tube to slow down. It is typically the case that the air parcels traveling over the upper surface will reach the trailing edge before those traveling over the bottom.

From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface. The pressure difference thus creates a net aerodynamic force, pointing upward and downstream to the flow direction. The component of the force normal to the freestream is considered to be lift; the component parallel to the freestream is drag. In conjunction with this force by the air on the airfoil, by Newton's third law, the airfoil imparts an equal-and-opposite force on the surrounding air that creates the downwash. Measuring the momentum transferred to the downwash is another way to determine the amount of lift on the airfoil.

Flowfield formation

In attempting to explain why the flow follows the upper surface of the airfoil, the situation gets considerably more complex. It is here that many simplifications are made in presenting lift to various audiences, some of which are explained after this section.

Consider the case of an airfoil accelerating from rest in a viscous flow. Lift depends entirely on the nature of viscous flow past certain bodies: in inviscid flow (i.e. assuming that viscous forces are negligible in comparison to inertial forces), there is no lift without imposing a net circulation, the proper amount of which can be determined by applying the Kutta condition. In a viscous flow like in the physical world, however, the lift and other properties arise naturally as described here.

When there is no flow, there is no lift and the forces acting on the airfoil are zero. At the instant when the flow is “turned on”, the flow is undeflected downstream of the airfoil and there are two stagnation points on the airfoil (where the flow velocity is zero): one near the leading edge on the bottom surface, and another on the upper surface near the trailing edge. The dividing line between the upper and lower streamtubes mentioned above intersects the body at the stagnation points. Since the flow speed is zero at these points, by Bernoulli's principle the static pressure at these points is at a maximum. As long as the second stagnation point is at its initial location on the upper surface of the wing, the circulation around the airfoil is zero and, in accordance with the Kutta–Joukowski theorem, there is no lift. The net pressure difference between the upper and lower surfaces is zero.

The effects of viscosity are contained within a thin layer of fluid called the boundary layer, close to the body. As flow over the airfoil commences, the flow along the lower surface turns at the sharp trailing edge and flows along the upper surface towards the upper stagnation point. The flow in the vicinity of the sharp trailing edge is very fast and the resulting viscous forces cause the boundary layer to accumulate into a vortex on the upper side of the airfoil between the trailing edge and the upper stagnation point. This is called the starting vortex. The starting vortex and the bound vortex around the surface of the wing are two halves of a closed loop. As the starting vortex increases in strength the bound vortex also strengthens, causing the flow over the upper surface of the airfoil to

accelerate and drive the upper stagnation point towards the sharp trailing edge. As this happens, the starting vortex is shed into the wake, and is a necessary condition to produce lift on an airfoil. If the flow were stopped, there would be a corresponding "stopping vortex". Despite being an idealization of the real world, the “vortex system” set up around a wing is both real and observable; the trailing vortex sheet most noticeably rolls up into wing-tip vortices.

The upper stagnation point continues moving downstream until it is coincident with the sharp trailing edge (as stated by the Kutta condition). The flow downstream of the airfoil is deflected downward from the free-stream direction and, from the reasoning above in the basic explanation, there is now a net pressure difference between the upper and lower surfaces and an aerodynamic force is generated.

Other alternative explanations for the generation of lift

It is amazing that today, almost 100 years after the first flight of the Wright Flyer, groups of engineers, scientists, pilots, and others can gather together and have a spirited debate on how an airplane wing generates lift. Various explanations are put forth, and the debate centers on which explanation is the most fundamental.

– John D. Anderson

Many other alternative explanations for the generation of lift by an airfoil have been put forward, of which a few are presented here. Most of them are intended to explain the phenomenon of lift to a general audience. Although the explanations may share features in common with the explanation above, additional assumptions and simplifications may be introduced. This can reduce the validity of an alternative explanation to a limited sub-class of lift generating conditions, or might not allow a quantitative analysis. Several theories introduce assumptions which proved to be wrong, like the equal transit-time theory.

"Popular" explanation based on equal transit-time

An illustration of the (incorrect) equal transit-time theory.

An explanation of lift frequently encountered in basic or popular sources is the equal transit-time theory. Equal transit-time states that because of the longer path of the upper surface of an airfoil, the air going over the top must go faster in order to catch up with the air flowing around the bottom. i.e. the parcels of air that are divided at the leading edge and travel above and below an airfoil must rejoin when they reach the trailing edge. Bernoulli's Principle is then cited to conclude that since the air moves faster on the top of the wing the air pressure must be lower. This pressure difference pushes the wing up.

However, equal transit time is not accurate and the fact that this is not generally the case can be readily observed. Although it is true that the air moving over the top of a wing generating lift does move faster, there is no requirement for equal transit time. In fact the air moving over the top of an airfoil generating lift is always moving much faster than the equal transit theory would imply.

The assertion that the air must arrive simultaneously at the trailing edge is sometimes referred to as the "Equal Transit-Time Fallacy".

Note that while this theory depends on Bernoulli's principle, the fact that this theory has been discredited does not imply that Bernoulli's principle is incorrect.

Coandă effect

In a limited sense, the Coandă effect refers to the tendency of a fluid jet to stay attached to an adjacent surface that curves away from the flow, and the resultant entrainment of ambient air into the flow. The effect is named for Henri Coandă, the Romanian aerodynamicist who exploited it in many of his patents.

One of the first known uses was in his patent for a high-lift device that used a fan of gas exiting at high speed from an internal compressor. This circular spray was directed radially over the top of a curved surface shaped like a lens to decrease the pressure on that surface. The total lift for the device was caused by the difference between this pressure and that on the bottom of the craft. Two aircraft, the Antonov An-72 and An-74 "Coaler", use the exhaust from top-mounted jet engines flowing over the wing to enhance lift, as did the Boeing YC-14 and the McDonnell Douglas YC-15. The effect is also used in high-lift devices such as a blown flap.

More broadly, some consider the effect to include the tendency of any fluid boundary layer to adhere to a curved surface, not just the boundary layer accompanying a fluid jet. It is in this broader sense that the Coandă effect is used by some to explain lift. Jef Raskin, for example, describes a simple demonstration, using a straw to blow over the upper surface of a wing. The wing deflects upwards, thus supposedly demonstrating that the Coandă effect creates lift. This demonstration correctly demonstrates the Coandă effect as a fluid jet (the exhaust from a straw) adhering to a curved surface (the wing). However, the upper surface in this flow is a complicated, vortex-laden mixing layer, while on the lower surface the flow is quiescent. The physics of this demonstration are very different from that of the general flow over the wing. The usage in this sense is

encountered in some popular references on aerodynamics. In the aerodynamics field, the Coandă effect is commonly defined in the more limited sense above and viscosity is used to explain why the boundary layer attaches to the surface of a wing.

In terms of a difference in areas

When a fluid flows relative to a solid body, the body obstructs the flow, causing some of the fluid to change its speed and direction in order to flow around the body. The obstructive nature of the solid body causes the streamlines to move closer together in some places, and further apart in others. When fluid flows past a 2-D cambered airfoil at zero angle of attack, the upper surface has a greater area (that is, the interior area of the airfoil above the chordline) than the lower surface and hence presents a greater obstruction to the fluid than the lower surface. This asymmetry causes the streamlines in the fluid flowing over the upper surface to move closer together than the streamlines over the lower surface. As a consequence of mass conservation, the reduced area between the streamlines over the upper surface results in a higher velocity than that over the lower surface. The upper streamtube is squashed the most in the nose region ahead of the maximum thickness of the airfoil, causing the maximum velocity to occur ahead of the maximum thickness.

In accordance with Bernoulli's principle, where the fluid is moving faster the pressure is lower, and where the fluid is moving slower the pressure is greater. The fluid is moving faster over the upper surface, particularly near the leading edge, than over the lower surface so the pressure on the upper surface is lower than the pressure on the lower surface. The difference in pressure between the upper and lower surfaces results in lift.

Methods to determine lift on an airfoil

Lift coefficient

If the lift coefficient for a wing at a specified angle of attack is known (or estimated using a method such as thin-airfoil theory), then the lift produced for specific flow conditions can be determined using the following equation:

where

• L is lift force, • ρ is air density • v is true airspeed, • A is planform area, and • CL is the lift coefficient at the desired angle of attack, Mach number, and

Reynolds number

This equation is basically the same as the drag equation, only the lift/drag coefficient is different.

Kutta–Joukowski theorem

Lift can be calculated using potential flow theory by imposing a circulation. It is often used by practicing aerodynamicists as a convenient quantity in calculations, for example thin-airfoil theory and lifting-line theory.

The circulation Γ is the line integral of the velocity of the air, in a closed loop around the boundary of an airfoil. It can be understood as the total amount of "spinning" (or vorticity) of air around the airfoil. The section lift/span L' can be calculated using the Kutta–Joukowski theorem:

where ρ is the air density, V is the free-stream airspeed. Kelvin's circulation theorem states that circulation is conserved. There is conservation of the air's angular momentum. When an aircraft is at rest, there is no circulation.

The challenge when using the Kutta–Joukowski theorem to determine lift is to determine the appropriate circulation for a particular airfoil. In practice, this is done by applying the Kutta condition, which uniquely prescribes the circulation for a given geometry and free-stream velocity.

A physical understanding of the theorem can be observed in the Magnus effect, which is a lift force generated by a spinning cylinder in a freestream. Here the necessary circulation is induced by the mechanical rotation acting on the boundary layer, causing it to induce a faster flow around one side of the cylinder and a slower flow around the other. The asymmetric distribution of airspeed around the cylinder then produces a circulation in the outer inviscid flow.

Pressure integration

The force on the wing can be examined in terms of the pressure differences above and below the wing, which can be related to velocity changes by Bernoulli's principle.

The total lift force is the integral of vertical pressure forces over the entire wetted surface area of the wing:

where:

• L is the lift,

• A is the wing surface area • p is the value of the pressure, • n is the normal unit vector pointing into the wing, and • k is the vertical unit vector, normal to the freestream direction.

The above lift equation neglects the skin friction forces, which typically have a negligible contribution to the lift compared to the pressure forces. By using the streamwise vector i parallel to the freestream in place of k in the integral, we obtain an expression for the pressure drag Dp (which includes induced drag in a 3D wing). If we use the spanwise vector j, we obtain the side force Y.

One method for calculating the pressure is Bernoulli's equation, which is the mathematical expression of Bernoulli's principle. This method ignores the effects of viscosity, which can be important in the boundary layer and to predict friction drag, which is the other component of the total drag in addition to Dp.

The Bernoulli principle states that the sum total of energy within a parcel of fluid remains constant as long as no energy is added or removed. It is a statement of the principle of the conservation of energy applied to flowing fluids.

A substantial simplification of this proposes that as other forms of energy changes are inconsequential during the flow of air around a wing and that energy transfer in/out of the air is not significant, then the sum of pressure energy and speed energy for any particular parcel of air must be constant. Consequently, an increase in speed must be accompanied by a decrease in pressure and vice-versa. It should be noted that this is not a causational relationship. Rather, it is a coincidental relationship, whatever causes one must also cause the other as energy can neither be created nor destroyed. It is named for the Dutch-Swiss mathematician and scientist Daniel Bernoulli, though it was previously understood by Leonhard Euler and others.

Bernoulli's principle provides an explanation of pressure difference in the absence of air density and temperature variation (a common approximation for low-speed aircraft). If the air density and temperature are the same above and below a wing, a naive application of the ideal gas law requires that the pressure also be the same. Bernoulli's principle, by including air velocity, explains this pressure difference. The principle does not, however, specify the air velocity. This must come from another source, e.g., experimental data.

In order to solve for the velocity of inviscid flow around a wing, the Kutta condition must be applied to simulate the effects of inertia and viscosity. The Kutta condition allows for

the correct choice among an infinite number of flow solutions that otherwise obey the laws of conservation of mass and conservation of momentum.

Lift forces on bluff bodies

Flow separation and a Von Kármán vortex street behind a circular cylinder. The flow is from the right to the left. Part of the cylinder can be seen at the right edge of the image. Two locations of flow separation from the cylinder are clearly visible.

The flow around bluff bodies may also generate lift, besides a strong drag force. For instance, the flow around a circular cylinder generates a Kármán vortex street: vortices being shed in an alternating fashion from each side of the cylinder. The oscillatory nature of the flow is reflected in the fluctuating lift force on the cylinder, whereas the mean lift force is negligible. The lift force frequency is characterised by the dimensionless Strouhal number, which depends (among others) on the Reynolds number of the flow.

For a flexible structure, this oscillatory lift force may induce vortex-induced vibrations. Under certain conditions — for instance resonance or strong spanwise correlation of the lift force — the resulting motion of the structure due to the lift fluctuations may be strongly enhanced. Such vibrations may pose problems, even collapse, in man-made tall structures like for instance industrial chimneys, if not properly taken care of in the design.

Drag (physics)

Shape and flow Form drag

Skin friction

0% 100%

~10% ~90%

~90% ~10%

100% 0%

In fluid dynamics, drag (sometimes called air resistance or fluid resistance) refers to forces that oppose the relative motion of an object through a fluid (a liquid or gas). Drag forces act in a direction opposite to the oncoming flow velocity. Unlike other resistive forces such as dry friction, which is nearly independent of velocity, drag forces depend on velocity.

For a solid object moving through a fluid, the drag is the component of the net aerodynamic or hydrodynamic force acting opposite to the direction of the movement. The component perpendicular to this direction is considered lift. Therefore drag opposes the motion of the object, and in a powered vehicle it is overcome by thrust.

In astrodynamics, and depending on the situation, atmospheric drag can be regarded as an inefficiency requiring expense of additional energy during launch of the space object or as a bonus simplifying return from orbit.

Types of drag Types of drag are generally divided into the following categories:

• parasitic drag, consisting of o form drag, o skin friction, o interference drag,

• lift-induced drag, and • wave drag (aerodynamics) or wave resistance (ship hydrodynamics).

The phrase parasitic drag is mainly used in aerodynamics, since for lifting wings drag is in general small compared to lift. For flow around bluff bodies, drag is most often dominating, and then the qualifier "parasitic" is meaningless. Form drag, skin friction and interference drag on bluff bodies are not coined as being elements of parasitic drag, but directly as elements of drag. Further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in the aviation perspective of drag, or in the design of either semi-planing or planing hulls. Wave drag occurs when a solid object is moving through a fluid at or near the speed of sound in that fluid — or in case there is a freely-moving fluid surface with surface waves radiating from the object, e.g. from a ship. Also, the amount of drag experienced by the ship is decided upon by the amount of surface area showing in the direction the ship is heading and the speed it is going up.

For high velocities — or more precisely, at high Reynolds numbers — the overall drag of an object is characterized by a dimensionless number called the drag coefficient, and is calculated using the drag equation. Assuming a more-or-less constant drag coefficient, drag will vary as the square of velocity. Thus, the resultant power needed to overcome this drag will vary as the cube of velocity. The standard equation for drag is one half the coefficient of drag multiplied by the fluid mass density, the cross sectional area of the specified item, and the square of the velocity.

Wind resistance is a layman's term used to describe drag. Its use is often vague, and is usually used in a relative sense (e.g., a badminton shuttlecock has more wind resistance than a squash ball).

Drag at high velocity

Explanation of drag by NASA.

The drag equation calculates the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000), also called quadratic drag. The equation is attributed to Lord Rayleigh, who originally used L2 in place of A (L being some length). The force on a moving object due to a fluid is:

where

is the force of drag, is the density of the fluid, is the speed of the object relative to the fluid, is the reference area, is the drag coefficient (a dimensionless parameter, e.g. 0.25 to 0.45 for a car)

The reference area A is often defined as the area of the orthographic projection of the object — on a plane perpendicular to the direction of motion — e.g. for objects with a simple shape, such as a sphere, this is the cross sectional area. Sometimes different reference areas are given for the same object in which case a drag coefficient corresponding to each of these different areas must be given.

In case of a wing, comparison of the drag to the lift force is easiest when the reference areas are the same, since then the ratio of drag to lift force is just the ratio of drag to lift coefficient. Therefore, the reference for a wing often is the planform (or wing) area rather than the frontal area.

For an object with a smooth surface, and non-fixed separation points — like a sphere or circular cylinder — the drag coefficient may vary with Reynolds number Re, even up to very high values (Re of the order 107). For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for Re > 3,500. Further the drag coefficient Cd is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere).

Power

The power required to overcome the aerodynamic drag is given by:

Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much

work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.

Velocity of a falling object

The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity v = 0 at time t = 0, is roughly given by a function involving a hyperbolic tangent (tanh):

The hyperbolic tangent has a limit value of one, for large time t. In other words, velocity asymptotically approaches a maximum value called the terminal velocity vt:

For a potato-shaped object of average diameter d and of density ρobj, terminal velocity is about

For objects of water-like density (raindrops, hail, live objects — animals, birds, insects, etc.) falling in air near the surface of the Earth at sea level, terminal velocity is roughly equal to

with d in metre and vt in m/s. For example, for a human body ( ~ 0.6 m) ~ 70 m/s, for a small animal like a cat ( ~ 0.2 m) ~ 40 m/s, for a small bird ( ~ 0.05 m) ~ 20 m/s, for an insect ( ~ 0.01 m) ~ 9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers is determined by Stokes law.

Terminal velocity is higher for larger creatures, and thus potentially more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a cricket impacting at its terminal velocity will probably be unharmed. This explains why small animals can fall from a large height and not be harmed.

Very low Reynolds numbers — Stokes' drag

Trajectories of three objects thrown at the same angle (70°). The black object does not experience any form of drag and moves along a parabola. The blue object experiences Stokes' drag, and the green object Newton drag.

The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, Re < 1). In this case, the force of drag is approximately proportional to velocity, but opposite in direction. The equation for viscous resistance is:

where:

is a constant that depends on the properties of the fluid and the dimensions of the object, and

is the velocity of the object

When an object falls from rest, its velocity will be

which asymptotically approaches the terminal velocity . For a given , heavier objects fall faster.

For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), George Gabriel Stokes derived an expression for the drag constant,

where:

is the Stokes radius of the particle, and is the fluid viscosity.

For example, consider a small sphere with radius = 0.5 micrometre (diameter = 1.0 µm) moving through water at a velocity of 10 µm/s. Using 10−3 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water.

Drag in aerodynamics

Lift induced drag

Induced drag vs. lift

Lift-induced drag (also called induced drag) is drag which occurs as the result of the creation of lift on a three-dimensional lifting body, such as the wing or fuselage of an airplane. Induced drag consists of two primary components, including drag due to the creation of vortices (vortex drag) and the presence of additional viscous drag (lift-induced viscous drag). The vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air of varying pressure on the upper and lower surfaces of the body, which is a necessary condition for the creation of lift.

With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. For an aircraft in flight, this means that as the angle of attack, and therefore the lift coefficient, increases to the point of stall, so does the lift-induced drag. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow on the surface of the body.

Parasitic drag

Parasitic drag (also called parasite drag) is drag caused by moving a solid object through a fluid. Parasitic drag is made up of multiple components including viscous pressure drag (form drag), and drag due to surface roughness (skin friction drag). Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag, which is sometimes described as a component of parasitic drag.

In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift, creating more drag. However, as speed increases the induced drag becomes much less, but parasitic drag increases because the fluid is flowing faster around protruding objects increasing friction or drag. At even higher speeds in the transonic, wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize endurance (minimum fuel consumption), or maximise gliding range in the event of an engine failure.

Power curve in aviation

The power curve: parasitic and induced drag vs. airspeed

The interaction of parasitic and induced drag vs. airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the power curve, and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires more thrust as speed decreases, rather than less. The consequences of being "behind the curve" in flight are important and are taught as part of pilot training. At the subsonic airspeeds where the "U" shape of this curve is significant, wave drag has not yet become a factor, and so it is not shown in the curve.

Wave drag in transonic and supersonic flow

Qualitative variation in Cd factor with Mach number for aircraft

Wave drag (also called compressibility drag) is drag which is created by the presence of a body moving at high speed through a compressible fluid. In aerodynamics, Wave drag consists of multiple components depending on the speed regime of the flight.

In transonic flight (Mach numbers greater than 0.5 and less than 1.0), wave drag is the result of the formation of shockwaves on the body, formed when areas of local supersonic (Mach number greater than 1.0) flow are created. In practice, supersonic flow occurs on bodies traveling well below the speed of sound, as the local speed of air on a body increases when it accelerates over the body, in this case above Mach 1.0. Therefore, aircraft flying at transonic speed often incur wave drag through the normal course of operation. In transonic flight, wave drag is commonly referred to as transonic compressibility drag. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at these speeds.

In supersonic flight (Mach numbers greater than 1.0), wave drag is the result of shockwaves present on the body, typically oblique shockwaves formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large, unattached shockwaves, or bow waves will instead form. Additionally, local areas of transonic flow behind the initial shockwave may occur at lower supersonic speeds, and can lead to the development of additional, smaller shockwaves present on the surfaces of other lifting bodies, similar to those found in transonic flows. In supersonic flow regimes, wave drag is commonly separated into two components, supersonic lift-dependent wave drag and supersonic volume-dependent wave drag.

The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the Sears-Haack Distribution. Similarly, for a fixed volume, the shape for minimum wave drag is the Von Karman Ogive.

Busemann's Biplane is not, in principle, subject to wave drag at all when operated at its design speed, but is incapable of generating lift.

d'Alembert's paradox In 1752 d'Alembert proved that potential flow, the 18th century state-of-the-art inviscid flow theory amenable to mathematical solutions, resulted in the prediction of zero drag. This was in contradiction with experimental evidence, and became known as d'Alembert's paradox. In the 19th century the Navier–Stokes equations for the description of viscous flow were developed by Saint-Venant, Navier and Stokes. Stokes derived the drag around a sphere at very low Reynolds numbers, the result of which is called Stokes law.

In the limit of high-Reynolds numbers the Navier–Stokes equations approach the inviscid Euler equations; of which the potential-flow solutions considered by d'Alembert are solutions. However, at high Reynolds numbers all experiments showed there is drag. Attempts to construct inviscid steady flow solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results.

The notion of boundary layers — introduced by Prandtl in 1904, founded on both theory and experiments — explained the causes of drag at high Reynolds numbers. The boundary layer is the thin layer of fluid close to the object's boundary, where viscous effects remain important when the viscosity becomes very small (or equivalently the Reynolds number becomes very large).

Chapter 7

Reynolds Number and Mach Number

Reynolds number

A vortex street around a cylinder. This occurs around cylinders, independently of the fluid, the cylinder size and the fluid speed, provided that there is a Reynolds number of between 250 and 200,000. Picture courtesy, Cesareo de La Rosa Siqueira.

In fluid mechanics, the Reynolds number Re is a dimensionless number that gives a measure of the ratio of inertial forces ρV2/L to viscous forces μV/L2 and consequently quantifies the relative importance of these two types of forces for given flow conditions. The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number is named after Osborne Reynolds (1842–1912), who popularized its use in 1883.

Reynolds numbers frequently arise when performing dimensional analysis of fluid dynamics problems, and as such can be used to determine dynamic similitude between different experimental cases. They are also used to characterize different flow regimes, such as laminar or turbulent flow: laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion, while turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.

Definition Reynolds number can be defined for a number of different situations where a fluid is in relative motion to a surface (the definition of the Reynolds number is not to be confused with the Reynolds Equation or lubrication equation). These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension. This dimension is a matter of convention - for example a radius or diameter are equally valid for spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is generally used today. Other shapes (such as rectangular pipes or non-spherical objects) have an equivalent diameter defined. For fluids of variable density (e.g. compressible gases) or variable viscosity (non-Newtonian fluids) special rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels.

where:

• is the mean fluid velocity (SI units: m/s) • L is a characteristic linear dimension, (traveled length of fluid, or hydraulic

diameter when dealing with river systems) (m) • μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s)) • ν is the kinematic viscosity (ν = μ / ρ) (m²/s) • is the density of the fluid (kg/m³)

And in pipes:

• Q is the volumetric flow rate (m3/s) • A is the pipe cross-sectional area (m²).

Note that this is equal to the ratio between , which is the drag (up to a numerical

factor, half the drag coefficient), and , which is the force due to viscosity (up to a numerical factor depending on the form of the flow).

Flow in Pipe

For flow in a pipe or tube, the Reynolds number is generally defined as:

where:

• DH is the hydraulic diameter of the pipe (m).

Flow in a non-circular duct (annulus)

For shapes such as squares, rectangular or annular ducts (where the height and width are comparable) the characteristic dimension for internal flow situations is taken to be the hydraulic diameter, DH, defined as 4 times the cross-sectional area (of the fluid), divided by the wetted perimeter. The wetted perimeter for a channel is the total perimeter of all channel walls that are in contact with the flow. This means the length of the water exposed to air is NOT included in the wetted perimeter

For a circular pipe, the hydraulic diameter is exactly equal to the inside pipe diameter, as can be shown mathematically.

For an annular duct, such as the outer channel in a tube-in-tube heat exchanger, the hydraulic diameter can be shown algebraically to reduce to

DH,annulus = Do − Di

where

Do is the inside diameter of the outside pipe, and Di is the outside diameter of the inside pipe.

For calculations involving flow in non-circular ducts, the hydraulic diameter can be substituted for the diameter of a circular duct, with reasonable accuracy.

Flow in a Wide Duct

For a fluid moving between two plane parallel surfaces (where the width is much greater than the space between the plates) then the characteristic dimension is twice the distance between the plates.

Flow in an Open Channel

For flow of liquid with a free surface, the hydraulic radius must be determined. This is the cross-sectional area of the channel divided by the wetted perimeter. For a semi-circular channel, it is half the radius. For a rectangular channel, the hydraulic radius is the cross-sectional area divided by the wetted perimeter. Some texts then use a characteristic dimension that is 4 times the hydraulic radius (chosen because it gives the same value of Re for the onset of turbulence as in pipe flow), while others the hydraulic radius as the

characteristic length-scale with consequently different values of Re for transition and turbulent flow.

Object in a fluid

The Reynolds number for an object in a fluid, called the particle Reynolds number and often denoted Rep, is important when considering the nature of flow around that grain, whether or not vortex shedding will occur, and its fall velocity.

Sphere in a fluid

For a sphere in a fluid, the characteristic length-scale is the diameter of the sphere and the characteristic velocity is that of the sphere relative to the fluid some distance away from the sphere (such that the motion of the sphere does not disturb that reference parcel of fluid). The density and viscosity are those belonging to the fluid. Note that purely laminar flow only exists up to Re = 0.1 under this definition.

Under the condition of low Re, the relationship between force and speed of motion is given by Stokes' law.

Oblong object in a fluid

The equation for an oblong object is identical to that of a sphere, with the object being approximated as an ellipsoid and the axis of *fix this* length being chosen as the characteristic length scale. Such considerations are important in natural streams, for example, where there are few perfectly spherical grains. For grains in which measurement of each axis is impractical (e.g., because they are too small), sieve diameters are used instead as the characteristic particle length-scale. Both approximations alter the values of the critical Reynolds number.

Fall velocity

The particle Reynolds number is important in determining the fall velocity of a particle. When the particle Reynolds number indicates laminar flow, Stokes' law can be used to calculate its fall velocity. When the particle Reynolds number indicates turbulent flow, a turbulent drag law must be constructed to model the appropriate settling velocity.

Packed Bed

For flow of fluid through a bed of approximately spherical particles of diameter D in contact, if the voidage (fraction of the bed not filled with particles) is ε and the superficial velocity V (i.e. the velocity through the bed as if the particles were not there - the actual velocity will be higher) than a Reynolds number can be defined as:

Laminar conditions apply up to Re = 10, fully turbulent from 2000.

Stirred Vessel

In a cylindrical vessel stirred by a central rotating paddle, turbine or propellor, the characteristic dimension is the diameter of the agitator D. The velocity is ND where N is the rotational speed (revolutions per second). Then the Reynolds number is:

The system is fully turbulent for values of Re above 10 000.

Transition Reynolds number In boundary layer flow over a flat plate, experiments can confirm that, after a certain length of flow, a laminar boundary layer will become unstable and become turbulent. This instability occurs across different scales and with different fluids, usually when

, where x is the distance from the leading edge of the flat plate, and the flow velocity is the freestream velocity of the fluid outside the boundary layer.

For flow in a pipe of diameter D, experimental observations show that for 'fully developed' flow (Note:), laminar flow occurs when ReD < 2300 and turbulent flow occurs when ReD > 4000. In the interval between 2300 and 4000, laminar and turbulent flows are possible ('transition' flows), depending on other factors, such as pipe roughness and flow uniformity). This result is generalised to non-circular channels using the hydraulic diameter, allowing a transition Reynolds number to be calculated for other shapes of channel.

These transition Reynolds numbers are also called critical Reynolds numbers, and were studied by Osborne Reynolds around 1895.

Reynolds number in pipe friction

Pressure drops seen for fully-developed flow of fluids through pipes can be predicted using the Moody diagram which plots the Darcy–Weisbach friction factor f against Reynolds number Re and relative roughness ε / D. The diagram clearly shows the laminar, transition, and turbulent flow regimes as Reynolds number increases. The nature of pipe flow is strongly dependent on whether the flow is laminar or turbulent

The similarity of flows In order for two flows to be similar they must have the same geometry, and have equal Reynolds numbers and Euler numbers. When comparing fluid behaviour at corresponding points in a model and a full-scale flow, the following holds:

quantities marked with 'm' concern the flow around the model and the others the actual flow. This allows engineers to perform experiments with reduced models in water channels or wind tunnels, and correlate the data to the actual flows, saving on costs during experimentation and on lab time. Note that true dynamic similitude may require

matching other dimensionless numbers as well, such as the Mach number used in compressible flows, or the Froude number that governs open-channel flows. Some flows involve more dimensionless parameters than can be practically satisfied with the available apparatus and fluids (for example air or water), so one is forced to decide which parameters are most important. For experimental flow modeling to be useful, it requires a fair amount of experience and judgement of the engineer.

Typical values of Reynolds number

• Bacteria ~ 1 x 10−5 • Spermatozoa ~ 1 x 10−4 • Ciliate ~ 1 x 10−1 • Smallest Fish ~ 1

• Blood flow in brain ~ 1 × 102 • Blood flow in aorta ~ 1 × 103

Onset of turbulent flow ~ 2.3 × 103 to 5.0 × 104 for pipe flow to 106 for boundary layers

• Typical pitch in Major League Baseball ~ 2 × 105 • Person swimming ~ 4 × 106 • Fastest Fish ~ 1 x 106 • Blue Whale ~ 3 × 108 • A large ship (RMS Queen Elizabeth 2) ~ 5 × 109

Reynolds number sets the smallest scales of turbulent motion In a turbulent flow, there is a range of scales of the time-varying fluid motion. The size of the largest scales of fluid motion (sometimes called eddies) are set by the overall geometry of the flow. For instance, in an industrial smoke stack, the largest scales of fluid motion are as big as the diameter of the stack itself. The size of the smallest scales is set by the Reynolds number. As the Reynolds number increases, smaller and smaller scales of the flow are visible. In a smoke stack, the smoke may appear to have many very small velocity perturbations or eddies, in addition to large bulky eddies. In this sense, the Reynolds number is an indicator of the range of scales in the flow. The higher the Reynolds number, the greater the range of scales. The largest eddies will always be the same size; the smallest eddies are determined by the Reynolds number.

What is the explanation for this phenomenon? A large Reynolds number indicates that viscous forces are not important at large scales of the flow. With a strong predominance of inertial forces over viscous forces, the largest scales of fluid motion are undamped—there is not enough viscosity to dissipate their motions. The kinetic energy must "cascade" from these large scales to progressively smaller scales until a level is reached for which the scale is small enough for viscosity to become important (that is, viscous

forces become of the order of inertial ones). It is at these small scales where the dissipation of energy by viscous action finally takes place. The Reynolds number indicates at what scale this viscous dissipation occurs. Therefore, since the largest eddies are dictated by the flow geometry and the smallest scales are dictated by the viscosity, the Reynolds number can be understood as the ratio of the largest scales of the turbulent motion to the smallest scales.

Example of the importance of the Reynolds number If an airplane wing needs testing, one can make a scaled down model of the wing and test it in a wind tunnel using the same Reynolds number that the actual airplane is subjected to. If for example the scale model has linear dimensions one quarter of full size, the flow velocity of the model would have to be multiplied by a factor of 4 to obtain similar flow behavior.

Alternatively, tests could be conducted in a water tank instead of in air (provided the compressibility effects of air are not significant). As the kinematic viscosity of water is around 13 times less than that of air at 15 °C, in this case the scale model would need to be about one thirteenth the size in all dimensions to maintain the same Reynolds number, assuming the full-scale flow velocity was used.

The results of the laboratory model will be similar to those of the actual plane wing results. Thus there is no need to bring a full scale plane into the lab and actually test it. This is an example of "dynamic similarity".

Reynolds number is important in the calculation of a body's drag characteristics. A notable example is that of the flow around a cylinder. Above roughly 3×106 Re the drag coefficient drops considerably. This is important when calculating the optimal cruise speeds for low drag (and therefore long range) profiles for airplanes.

Reynolds number in physiology Poiseuille's law on blood circulation in the body is dependent on laminar flow. In turbulent flow the flow rate is proportional to the square root of the pressure gradient, as opposed to its direct proportionality to pressure gradient in laminar flow.

Using the definition of the Reynolds number we can see that a large diameter with rapid flow, where the density of the blood is high, tends towards turbulence. Rapid changes in vessel diameter may lead to turbulent flow, for instance when a narrower vessel widens to a larger one. Furthermore, an atheroma may be the cause of turbulent flow, and as such detecting turbulence with a stethoscope may be a sign of such a condition.

Reynolds number in viscous fluids

Creeping flow past a sphere: streamlines, drag force Fd and force by gravity Fg.

Where the viscosity is naturally high, such as polymer solutions and polymer melts, flow is normally laminar. The Reynolds number is very small and Stokes' Law can be used to measure the viscosity of the fluid. Spheres are allowed to fall through the fluid and they reach the terminal velocity quickly, from which the viscosity can be determined.

The laminar flow of polymer solutions is exploited by animals such as fish and dolphins, who exude viscous solutions from their skin to aid flow over their bodies while swimming. It has been used in yacht racing by owners who want to gain a speed advantage by pumping a polymer solution such as low molecular weight polyoxyethylene

in water, over the wetted surface of the hull. It is however, a problem for mixing of polymers, because turbulence is needed to distribute fine filler (for example) through the material. Inventions such as the "cavity transfer mixer" have been developed to produce multiple folds into a moving melt so as to improve mixing efficiency. The device can be fitted onto extruders to aid mixing.

Where does it come from? The Reynolds number can be obtained when one uses the nondimensional form of the incompressible Navier-Stokes equations:

Each term in the above equation has the units of a volume force or, equivalently, an acceleration times a density. Each term is thus dependent on the exact measurements of a flow. When one renders the equation nondimensional, that is that we multiply it by a factor with inverse units of the base equation, we obtain a form which does not depend directly on the physical sizes. One possible way to obtain a nondimensional equation is to multiply the whole equation by the following factor:

where the symbols are the same as those used in the definition of the Reynolds number. If we now set:

we can rewrite the Navier-Stokes equation without dimensions:

where the term:

Finally, dropping the primes for ease of reading:

This is why mathematically all flows with the same Reynolds number are comparable. Notice also, in the above equation, as: the viscous terms vanish. Thus, high Reynolds number flows are approximately inviscid in the free-stream.

Mach number

An F/A-18 Hornet at transonic speed and displaying the Prandtl–Glauert singularity just before reaching the speed of sound

Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure. It is commonly used to represent the speed of an object when it is travelling close to or above the speed of sound.

where

is the Mach number is the speed of the source (the object relative to the medium) and

is the speed of sound in the medium

The Mach number is named after Austrian physicist and philosopher Ernst Mach. Because the Mach number is often viewed as a dimensionless quantity rather than a unit of measure, with Mach, the number comes after the unit; the second Mach number is

"Mach 2" instead of "2 Mach" (or Machs). This is somewhat reminiscent of the early modern ocean sounding unit "mark" (a synonym for fathom), which was also unit-first, and may have influenced the use of the term Mach. In the decade preceding faster-than-sound human flight, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1."

Overview The Mach number is commonly used both with objects traveling at high speed in a fluid, and with high-speed fluid flows inside channels such as nozzles, diffusers or wind tunnels. As it is defined as a ratio of two speeds, it is a dimensionless number. At a temperature of 15 degrees Celsius the speed of sound is 340.3 m/s (1225 km/h, or 761.2 mph, or 661.5 knots, or 1116 ft/s) in the Earth's atmosphere. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature and atmospheric composition and largely independent of pressure. In the stratosphere, where the temperatures are constant, it does not vary with altitude even though the air pressure changes significantly with altitude.

Since the speed of sound increases as the temperature increases, the actual speed of an object traveling at Mach 1 will depend on the fluid temperature around it. Mach number is useful because the fluid behaves in a similar way at the same Mach number. So, an aircraft traveling at Mach 1 at 20°C or 68°F will experience shock waves in much the same manner as when it is traveling at Mach 1 at 11,000 m (36,000 ft) at -50°C or -58F, even though it is traveling at only 86% of its speed at higher temperature like 20°C or 68°F.

High-speed flow around objects Flight can be roughly classified in six categories:

Regime Subsonic Transonic Sonic Supersonic Hypersonic High-hypersonic

Mach <0.75 0.75–1.2 1.0 1.2–5.0 5.0–10.0 >10.0

For comparison: the required speed for low Earth orbit is approximately 7.5 km/s = Mach 25.4 in air at high altitudes. The speed of light in a vacuum corresponds to a Mach number of approximately 881,000 (relative to air at sea level).

At transonic speeds, the flow field around the object includes both sub- and supersonic parts. The transonic period begins when first zones of M>1 flow appear around the object. In case of an airfoil (such as an aircraft's wing), this typically happens above the wing. Supersonic flow can decelerate back to subsonic only in a normal shock; this typically happens before the trailing edge. (Fig.1a)

As the speed increases, the zone of M>1 flow increases towards both leading and trailing edges. As M=1 is reached and passed, the normal shock reaches the trailing edge and becomes a weak oblique shock: the flow decelerates over the shock, but remains supersonic. A normal shock is created ahead of the object, and the only subsonic zone in the flow field is a small area around the object's leading edge. (Fig.1b)

(a) (b)

Fig. 1. Mach number in transonic airflow around an airfoil; M<1 (a) and M>1 (b).

When an aircraft exceeds Mach 1 (i.e. the sound barrier) a large pressure difference is created just in front of the aircraft. This abrupt pressure difference, called a shock wave, spreads backward and outward from the aircraft in a cone shape (a so-called Mach cone). It is this shock wave that causes the sonic boom heard as a fast moving aircraft travels overhead. A person inside the aircraft will not hear this. The higher the speed, the more narrow the cone; at just over M=1 it is hardly a cone at all, but closer to a slightly concave plane.

At fully supersonic speed, the shock wave starts to take its cone shape and flow is either completely supersonic, or (in case of a blunt object), only a very small subsonic flow area remains between the object's nose and the shock wave it creates ahead of itself. (In the case of a sharp object, there is no air between the nose and the shock wave: the shock wave starts from the nose.)

As the Mach number increases, so does the strength of the shock wave and the Mach cone becomes increasingly narrow. As the fluid flow crosses the shock wave, its speed is reduced and temperature, pressure, and density increase. The stronger the shock, the greater the changes. At high enough Mach numbers the temperature increases so much over the shock that ionization and dissociation of gas molecules behind the shock wave begin. Such flows are called hypersonic.

It is clear that any object traveling at hypersonic speeds will likewise be exposed to the same extreme temperatures as the gas behind the nose shock wave, and hence choice of heat-resistant materials becomes important.

High-speed flow in a channel As a flow in a channel crosses M=1 becomes supersonic, one significant change takes place. The conservation of mass flow rate leads one to expect that contracting the flow channel would increase the flow speed (i.e. making the channel narrower results in faster air flow) and at subsonic speeds this holds true. However, once the flow becomes supersonic, the relationship of flow area and speed is reversed: expanding the channel actually increases the speed.

The obvious result is that in order to accelerate a flow to supersonic, one needs a convergent-divergent nozzle, where the converging section accelerates the flow to M=1, sonic speeds, and the diverging section continues the acceleration. Such nozzles are called de Laval nozzles and in extreme cases they are able to reach incredible, hypersonic speeds (Mach 13 at 20°C).

An aircraft Machmeter or electronic flight information system (EFIS) can display Mach number derived from stagnation pressure (pitot tube) and static pressure.

Calculating Mach Number Assuming air to be an ideal gas, the formula to compute Mach number in a subsonic compressible flow is derived from Bernoulli's equation for M<1:

where:

is Mach number is impact pressure and is static pressure

is the ratio of specific heat of a gas at a constant pressure to heat at a constant volume (1.4 for air).

The Mach number at which an aircraft is flying at can be calculated by

where:

is Mach number is velocity of the moving aircraft and

is the speed of sound at the given altitude

The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:

where:

is now impact pressure measured behind a normal shock.

Chapter 8

Compressible Aerodynamics

1. Transonic

F/A-18 flying at transonic speed

Although they may not look like it, most modern jet aircraft's shape is based on trying to keep close to the same cross-sectional area as that of a Sears-Haack body along their entire length

Transonic flow patterns on an airfoil showing flow patterns at and above critical Mach number.

Transonic flow patterns on F-16 fighter aircraft

Transonic flow patterns on F-16 fighter aircraft

Transonic is an aeronautics term referring to the condition in which a range of velocities of airflow exist surrounding and flowing past an air vehicle or an airfoil. Air flow velocities are concurrently below, at, and above the speed of sound at the pressure and temperature of the airflow of the air vehicle's local environment (about mach 0.8–1.2, i.e. 600-900 mph). It is formally defined as the range of speeds between the critical Mach number, when some parts of the airflow over an air vehicle or air foil are supersonic, and a higher speed, typically near Mach 1.2, when all of the airflow is supersonic. Between these speeds some of the airflow is supersonic, and some is not.

Most modern jet powered aircraft are engineered to operate at transonic air speeds. Transonic airspeeds see a rapid increase of drag from about Mach 0.8, and it is the fuel costs of the drag that typically limits the airspeed. Attempts to reduce wave drag can be seen on all high-speed aircraft; most notable is the use of swept wings, but another common form is a wasp-waist fuselage as a side effect of the Whitcomb area rule.

Severe instability can occur at transonic speeds. Shock waves move through the air at the speed of sound. When an object such as an aircraft also moves at the speed of sound, these shock waves build up in front of it to form a single, very large shock wave. During transonic flight, the plane must pass through this large shock wave, as well as contending with the instability caused by air moving faster than sound over parts of the wing and slower in other parts. The difference in speed is due to Bernoulli's principle.

Transonic speeds can also occur at the tips of rotor blades of helicopters and aircraft. However, as this puts severe, unequal stresses on the rotor blade, it is avoided and may lead to dangerous accidents if it occurs. It is one of the limiting factors to the size of

rotors, and also to the forward speeds of helicopters (as this speed is added to the forward-sweeping (leading) side of the rotor, thus possibly causing localized transonics).

Condensation clouds At transonic speeds intense low-pressure areas form at various points around an aircraft. If conditions are right (i.e. high humidity) visible clouds will form in these low-pressure areas as shown in the illustration; these are called Prandtl-Glauert singularities. These clouds remain with the aircraft as it travels. It is not necessary for the aircraft as a whole to reach supersonic speeds for these clouds to form.

Transonic flows in astronomy and astrophysics In astrophysics, wherever there is evidence of shocks (standing, propagating or oscillating), the flow close by must be transonic as only supersonic flows form shocks. Interestingly all the black hole accretions are transonic (S.K. Chakrabarti, ApJ, 1996, v. 471, p. 237), many of the flows also have shocks very close to the black holes.

The outflows or jets from young stellar objects or disks around black holes can also be transonic since they start subsonically and at a far distance they are invariably supersonic. Supernovae explosion is accompanied by supersonic flows and shock waves. Bow shocks formed in solar winds around the earth are a direct result of transonic wind from the sun.

2. Supersonic

A United States Navy F/A-18E/F Super Hornet in transonic flight.

U.S. Navy F/A-18 approaching the sound barrier. The white halo is formed by condensed water droplets which result from the shockwave shedding from the aircraft.

The term supersonic is used to define a speed that is over the speed of sound (Mach 1). In dry air at 20 °C (68 °F), the threshold value required for an object to be traveling at a supersonic speed is approximately 343 m/s, (1,125 ft/s, 768 mph or 1,236 km/h). Speeds greater than 5 times the speed of sound (Mach 5) are often referred to as hypersonic. Speeds where only some parts of the air around an object (such as the ends of rotor blades) reach supersonic speeds are labeled transonic (typically somewhere between Mach 0.8 and Mach 1.2).

Sounds are travelling vibrations (pressure waves) in an elastic medium. In gases sound travels longitudinally at different speeds, mostly depending on the molecular mass and temperature of the gas; (pressure has little effect). Since air temperature and composition varies significantly with altitude, Mach numbers for aircraft can change without airspeed varying. In water at room temperature supersonic can be considered as any speed greater than 1,440 m/s (4,724 ft/s). In solids, sound waves can be longitudinal or transverse and have even higher velocities. Supersonic fracture is crack motion faster than the speed of sound in a brittle material.

Supersonic objects Most modern fighter aircraft are supersonic, but there have been supersonic passenger aircraft, namely Concorde and the Tupolev Tu-144. Both these passenger aircraft and some modern fighters are also capable of supercruise, a condition of sustained supersonic flight without the use of an afterburner. Due to its ability to supercruise for several hours and the relatively high frequency of flight over several decades, Concorde spent more time flying supersonically than all other aircraft put together by a considerable margin. Since Concorde's final retirement flight on November 26, 2003, there are no supersonic passenger aircraft left in service. Some large bombers, such as the Tupolev Tu-160 and Rockwell/Boeing B-1B are also supersonic-capable.

Most modern firearm bullets are supersonic, with rifle projectiles often travelling at speeds approaching and in some cases largely exceeding Mach 3.

Most spacecraft, most notably the Space Shuttle are supersonic at least during portions of their reentry, though the effects on the spacecraft are reduced by low air pressures. During ascent, launch vehicles generally avoid going supersonic below 30 km (~98,400 feet) to reduce air drag.

Note that the speed of sound decreases somewhat with altitude, due to lower temperatures found there (typically up to 25 km). At even higher altitudes the temperature starts increasing, with the corresponding increase in the speed of sound.

A wave traveling through a bull whip is also capable of achieving supersonic speeds.

Supersonic flight Supersonic aerodynamics are simpler than subsonic because the airsheets at different points along the plane often can't affect each other. Supersonic jets and rocket vehicles require several times greater thrust to push through the extra drag experienced within the transonic region (around Mach 0.85-1.2). At these speeds aerospace engineers can gently guide air around the fuselage of the aircraft without producing new shock waves but any change in cross sectional area further down the vehicle leads to shock waves along the body. Designers use the Supersonic area rule and the Whitcomb area rule to minimize sudden changes in size.

It should be kept in mind, however, that the aerodynamic principles behind a supersonic aircraft are often more complex than described above because such an aircraft must be efficient and stable at supersonic, transonic and subsonic flight.

One problem with sustained supersonic flight is the generation of heat in flight. At high speeds aerodynamic heating can occur, so an aircraft must be designed to operate and function under very high temperatures. Duralumin, the traditional aircraft material, starts to lose strength and go into plastic deformation at relatively low temperatures, and is

unsuitable for continuous use at speeds above Mach 2.2 to 2.4. Materials such as titanium and stainless steel allow operations at much higher temperatures. For example, the SR-71 Blackbird jet could fly continuously at Mach 3.1 while some parts were above 315°C (600°F).

Another area of concern for continued high-speed operation is the engines. Jet engines create thrust by increasing the temperature of the air they ingest, and as the aircraft speeds up, friction and compression heats this air before it reaches the engines. The maximum temperature of the exhaust is determined by the materials in the turbine at the rear of the engine, so as the aircraft speeds up the difference in intake and exhaust temperature the engine can extract decreases, and the thrust along with it. Air cooling the turbine area to allow operations at higher temperatures was a key solution, one that continued to improve through the 1950s and on to this day.

Intake design was also a major issue. Normal jet engines can only ingest subsonic air, so for supersonic operation the air has to be slowed down. Ramps or cones in the intake are used to create shock waves that slows the airflow before it reaches the engine. Doing so removes energy from the airflow, causing drag. The key to reducing this drag is to use multiple small oblique shock waves, but this was difficult because the angle they make inside the intake changes with Mach number. In order to efficiently operate across a range of speeds, the shock waves have to be "tuned."

An aircraft able to operate for extended periods at supersonic speeds has a potential range advantage over a similar design operating subsonically. Most of the drag an aircraft sees while speeding up to supersonic speeds occurs just below the speed of sound, due to an aerodynamic effect known as wave drag. An aircraft that can accelerate past this speed sees a significant drag decrease, and can fly supersonically with improved fuel economy. However, due to the way lift is generated supersonically, the lift-to-drag ratio of the aircraft as a whole drops, leading to lower range, offsetting or overturning this advantage.

The key to having low supersonic drag is to properly shape the overall aircraft to be long and skinny, and close to a "perfect" shape, the von Karman ogive or Sears-Haack body. This has led to almost every supersonic cruising aircraft looking very similar to every other, with a very long and skinny fuselage and large delta wings, cf. SR-71, Concorde, etc. Although not ideal for passenger aircraft, this shaping is quite adaptable for bomber use.

History of supersonic flight

John Stack led the research on the "transonic gap" at NACA in the 1930s.

President Kennedy honors Dr. von Kármán.

The Hungarian-born American scientist Theodore Karman (May 11, 1881 – May 7, 1963) was the inventor of the mathematical tools to study fluid flow, the mathematical background of supersonic flight, and the swept-back wing. He is often called "the father of Supersonic Flight" due to his work on the stability of laminar flow, turbulence, airfoils in steady and unsteady flow, boundary layers, and supersonic aerodynamics, largely taking place in the 1940s through 60s.

The speed of sound was exceeded for the first time by a manned aircraft in controlled, level flight on October 14th, 1947 in an American research project, using the experimental Bell X-1 research rocket plane, piloted by Charles "Chuck" Yeager. The first production plane to break the sound barrier was an F-86 Canadair Sabre with the first 'supersonic' woman pilot, Jacqueline Cochran, at the controls, although this aircraft was not designed with regular supersonic flights in mind.

3. Hypersonic

Boeing X-43 at Mach 7

In aerodynamics, hypersonic speeds are those that are highly supersonic. Since the 1970s, the term has generally been assumed to refer to speeds of Mach 5 (5 times the speed of sound) and above. The hypersonic regime is a subset of the supersonic regime.

The precise Mach number at which a craft can be said to be fully hypersonic is elusive, especially since physical changes in the airflow (molecular dissociation, ionization) occur at quite different speeds. Generally, a combination of effects become important "as a whole" around Mach 5. The hypersonic regime is often defined as speeds where ramjets do not produce net thrust. This is a nebulous definition in itself, as there exists a proposed change to allow them to operate in the hypersonic regime (the Scramjet).

Characteristics of flow While the definition of hypersonic flow can be quite vague and is generally debatable (especially due to the lack of discontinuity between supersonic and hypersonic flows), a hypersonic flow may be characterized by certain physical phenomena that can no longer be analytically discounted as in supersonic flow. the peculiarity in hypersonic flows are as follows: 1. Shock Layer 2. Aerodynamic Heating 3. Entropy Layer 4. Real gas Effects 5. Low density Effects 6. Independence of Aerodynamic Co-efficients with Mach no.

Small shock stand-off distance

As a body's Mach number increases, the density behind the shock generated by the body also increases, which corresponds to a decrease in volume behind the shock wave due to conservation of mass. Consequently, the distance between the shock and the body decreases at higher Mach numbers.

Entropy layer

As Mach numbers increase, the entropy change across the shock also increases, which results in a strong entropy gradient and highly vortical flow that mixes with the boundary layer.

Viscous interaction

A portion of the large kinetic energy associated with flow at high Mach numbers transforms into internal energy in the fluid due to viscous effects. The increase in internal energy is realized as an increase in temperature. Since the pressure gradient normal to the flow within a boundary layer is approximately zero for low to moderate hypersonic Mach numbers, the increase of temperature through the boundary layer coincides with a decrease in density. Thus, the boundary layer over the body grows and can often merge with the thin shock layer.

High temperature flow

High temperatures discussed previously as a manifestation of viscous dissipation cause non-equilibrium chemical flow properties such as dissociation and ionization of molecules resulting in convective and radiative heat flux.

Effects The hypersonic flow regime is characterized by a number of effects which are not found in typical aircraft operating at low subsonic. The effects depend strongly on the speed and type of vehicle under investigation.

Classification of Mach regimes While the terms "subsonic" and "supersonic" in the purest verbal sense refer to speeds below and above the local speed of sound respectively, aerodynamicists often use the same terms to talk about particular ranges of Mach values. This occurs because of the presence of a "transonic regime" around M=1 where approximations of the Navier-Stokes equations used for subsonic design actually no longer apply, the simplest of many reasons being that the flow locally begins to exceed M=1 even when the freestream Mach number is below this value.

Meanwhile, the "supersonic regime" is usually used to talk about the set of Mach numbers for which linearised theory may be used, where for example the (air) flow is not chemically reacting, and where heat-transfer between air and vehicle may be reasonably neglected in calculations.

In the following table, the "regimes" or "ranges of Mach values" are referred to, and not the "pure" meanings of the words "subsonic" and "supersonic".

Generally, NASA defines "high" hypersonic as any Mach number from 10 to 25, and re-entry speeds as anything greater than Mach 25. Aircraft operating in this regime include the Space Shuttle and various space planes in development.

Regime Mach mph km/h m/s General plane characteristics

Subsonic <0.8 <768 <1,230 <340

Most often propeller-driven and commercial turbofan aircraft with high aspect-ratio (slender) wings, and rounded features like the nose and leading edges.

Transonic 0.8-1.2 610-768 980-

1,475 270-410

Transonic aircraft nearly always have swept wings, delaying drag-divergence, and often feature design adhering to the principles of the Whitcomb Area-Rule. Note that designing aircraft for use at M=1.1 for example, is very odd because of the very poor efficiency of flying at these speeds for basically any design, compared to flying at low-supersonic speeds, say M=1.6.

Supersonic 1.2-5.0

768-3,840

1,230-6,150

340-1,710

Aircraft designed to fly at supersonic speeds show large differences in their aerodynamic design because of the radical differences in the behaviour of flows above Mach 1. Sharp edges, thin aerofoil-sections, and all-moving tailplane/canards are typical. Modern combat aircraft must compromise in order to maintain low-speed handling; "true" supersonic designs include the F-104 Starfighter and BAC/Aérospatiale Concorde.

Hypersonic 5.0-10.0

3,840-7,680

6,150-12,300

1,710-3,415

Cooled nickel-titanium skin; highly integrated (due to domination of interference effects: non-linear behaviour means that superposition of results for separate components is invalid), small wings

High- 10.0- 7,680- 12,300- 3,415- Thermal control becomes a dominant

hypersonic 25.0 16,250 30,740 8,465 design consideration. Structure must either be designed to operate hot, or be protected by special silicate tiles or similar. Chemically reacting flow can also cause corrosion of the vehicle's skin, with free-atomic oxygen featuring in very high-speed flows. Hypersonic designs are often forced into blunt configurations because of the aerodynamic heating rising with a reduced radius of curvature.

Re-entry speeds >25.0 >16,250 >30,740 >8,465 Ablative heat shield; no wings; blunt

capsule shape

Similarity parameters The categorization of airflow relies on a number of similarity parameters, which allow the simplification of a nearly infinite number of test cases into groups of similarity. For transonic and compressible flow, the Mach and Reynolds numbers alone allow good categorization of many flow cases.

Hypersonic flows, however, require other similarity parameters. Firstly, the analytic equations for the Oblique shock angle become nearly independent of Mach number at high (~>10) Mach numbers. Secondly, the formation of strong shocks around aerodynamic bodies mean that the freestream Reynolds number is less useful as an estimate of the behavior of the boundary layer over a body (although it is still important). Finally, the increased temperature of hypersonic flows mean that real gas effects become important. For this reason, research in hypersonics is often referred to as aerothermodynamics, rather than aerodynamics.

The introduction of real gas effects mean that more variables are required to describe the full state of a gas. Whereas a stationary gas can be described by three variables (pressure, temperature, adiabatic index), and a moving gas by four (velocity), a hot gas in chemical equilibrium also requires state equations for the chemical components of the gas, and a gas in nonequilibrium solves those state equations using time as an extra variable. This means that for a nonequilibrium flow, something between 10 and 100 variables may be required to describe the state of the gas at any given time. Additionally, rarefied hypersonic flows (usually defined as those with a Knudsen number above 0.1) do not follow the Navier-Stokes equations.

Hypersonic flows are typically categorized by their total energy, expressed as total enthalpy (MJ/kg), total pressure (kPa-MPa), stagnation pressure (kPa-MPa), stagnation temperature (K), or velocity (km/s).

Wallace D. Hayes developed a similarity parameter, similar to the Whitcomb area rule, which allowed similar configurations to be compared.

Regimes Hypersonic flow can be approximately separated into a number of regimes. The selection of these regimes is rough, due to the blurring of the boundaries where a particular effect can be found.

Perfect gas

In this regime, the gas can be regarded as an ideal gas. Flow in this regime is still Mach number dependent. Simulations start to depend on the use of a constant-temperature wall, rather than the adiabatic wall typically used at lower speeds. The lower border of this region is around Mach 5, where Ramjets become inefficient, and the upper border around Mach 10-12.

Two-temperature ideal gas

This is a subset of the perfect gas regime, where the gas can be considered chemically perfect, but the rotational and vibrational temperatures of the gas must be considered separately, leading to two temperature models.

Dissociated gas

In this regime, diatomic or polyatomic gases (the gases found in most atmospheres) begin to dissociate as they come into contact with the bow shock generated by the body. Surface catalycity plays a role in the calculation of surface heating, meaning that the type of surface material also has an effect on the flow. The lower border of this regime is where any component of a gas mixture first begins to dissociate in the stagnation point of a flow (which for nitrogen is around 2000 K). At the upper border of this regime, the effects of ionization start to have an effect on the flow.

Ionized gas

In this regime the ionized electron population of the stagnated flow becomes significant, and the electrons must be modeled separately. Often the electron temperature is handled separately from the temperature of the remaining gas components. This region occurs for freestream velocities around 10-12 km/s. Gases in this region are modeled as non-radiating plasmas.

Radiation-dominated regime

Above around 12 km/s, the heat transfer to a vehicle changes from being conductively dominated to radiatively dominated. The modeling of gases in this regime is split into two classes:

1. Optically thin: where the gas does not re-absorb radiation emitted from other parts of the gas

2. Optically thick: where the radiation must be considered as a separate source of energy.

The modeling of optically thick gases is extremely difficult, since, due to the calculation of the radiation at each point, the computation load theoretically expands exponentially as the number of points considered increases.