Though the term "aerodynamics" is most commonly associated with airplanes and the overall science of flight, in fact, its application is much broader. Simply put, aerodynamics is the study of airflow and its principles, and applied aerodynamics is the science of improving manmade objects such as airplanes and automobiles in light of those principles. Aside from the obvious application to these heavy forms of transportation, aerodynamic concepts are also reflected in the simplest of manmade flying objects—and in the natural model for all studies of flight, a bird's wings.
HOW IT WORKS
All physical objects on Earth are subject to gravity, but gravity is not the only force that tends to keep them pressed to the ground. The air itself, though it is invisible, operates in such a way as to prevent lift, much as a stone dropped into the water will eventually fall to the bottom. In fact, air behaves much like water, though the downward force is not as great due to the fact that air's pressure is much less than that of water. Yet both are media through which bodies travel, and air and water have much more in common with one another than either does with a vacuum.
Liquids such as water and gasses such as air are both subject to the principles of fluid dynamics, a set of laws that govern the motion of liquids and vapors when they come in contact with solid surfaces. In fact, there are few significant differences—for the purposes of the present discussion—between water and air with regard to their behavior in contact with solid surfaces.
When a person gets into a bathtub, the water level rises uniformly in response to the fact that a solid object is taking up space. Similarly, air currents blow over the wings of a flying aircraft in such a way that they meet again more or less simultaneously at the trailing edge of the wing. In both cases, the medium adjusts for the intrusion of a solid object. Hence within the parameters of fluid dynamics, scientists typically use the term "fluid" uniformly, even when describing the movement of air.
The study of fluid dynamics in general, and of air flow in particular, brings with it an entire vocabulary. One of the first concepts of importance is viscosity, the internal friction in a fluid that makes it resistant to flow and resistant to objects flowing through it. As one might suspect, viscosity is a far greater factor with water than with air, the viscosity of which is less than two percent that of water. Nonetheless, near a solid surface—for example, the wing of an airplane—viscosity becomes a factor because air tends to stick to that surface.
Also significant are the related aspects of density and compressibility. At speeds below 220 MPH (354 km/h), the compressibility of air is not a significant factor in aerodynamic design. However, as air flow approaches the speed of sound—660 MPH (1,622 km/h)—compressibility becomes a significant factor. Likewise temperature increases greatly when airflow is supersonic, or faster than the speed of sound.
All objects in the air are subject to two types of airflow, laminar and turbulent. Laminar flow is smooth and regular, always moving at the same speed and in the same direction. This type of airflow is also known as streamlined flow, and under these conditions every particle of fluid that passes a particular point follows a path identical to all particles that passed that point earlier. This may be illustrated by imagining a stream flowing around a twig.
By contrast, in turbulent flow the air is subject to continual changes in speed and direction—as for instance when a stream flows over shoals of rocks. Whereas the mathematical model of laminar airflow is rather straightforward, conditions are much more complex in turbulent flow, which typically occurs in the presence either of obstacles or of high speeds.
Absent the presence of viscosity, and thus in conditions of perfect laminar flow, an object behaves according to Bernoulli's principle, sometimes known as Bernoulli's equation. Named after the Swiss mathematician and physicist Daniel Bernoulli (1700-1782), this proposition goes to the heart of that which makes an airplane fly.
While conducting experiments concerning the conservation of energy in liquids, Bernoulli observed that when the diameter of a pipe is reduced, the water flows faster. This suggested to him that some force must be acting upon the water, a force that he reasoned must arise from differences in pressure. Specifically, the slower-moving fluid had a greater pressure than the portion of the fluid moving through the narrower part of the pipe. As a result, he concluded that pressure and velocity are inversely related.
Bernoulli's principle states that for all changes in movement, the sum of static and dynamic pressure in a fluid remain the same. A fluid at rest exerts static pressure, which is the same as what people commonly mean when they say "pressure," as in "water pressure." As the fluid begins to move, however, a portion of the static pressure—proportional to the speed of the fluid—is converted to what scientists call dynamic pressure, or the pressure of movement. The greater the speed, the greater the dynamic pressure and the less the static pressure. Bernoulli's findings would prove crucial to the design of aircraft in the twentieth century, as engineers learned how to use currents of faster and slower air for keeping an airplane aloft.
Very close to the surface of an object experiencing airflow, however, the presence of viscosity plays havoc with the neat proportions of the Bernoulli's principle. Here the air sticks to the object's surface, slowing the flow of nearby air and creating a "boundary layer" of slow-moving air. At the beginning of the flow—for instance, at the leading edge of an airplane's wing—this boundary layer describes a laminar flow; but the width of the layer increases as the air moves along the surface, and at some point it becomes turbulent.
These and a number of other factors contribute to the coefficients of drag and lift. Simply put, drag is the force that opposes the forward motion of an object in airflow, whereas lift is a force perpendicular to the direction of the wind, which keeps the object aloft. Clearly these concepts can be readily applied to the operation of an airplane, but they also apply in the case of an automobile, as will be shown later.
How a Bird Flies—and Why a Human Being Cannot
Birds are exquisitely designed (or adapted) for flight, and not simply because of the obvious fact that they have wings. Thanks to light, hollow bones, their body weight is relatively low, giving them the advantage in overcoming gravity and remaining aloft. Furthermore, a bird's sternum or breast bone, as well as its pectoralis muscles (those around the chest) are enormous in proportion to its body size, thus helping it to achieve the thrust necessary for flight. And finally, the bird's lightweight feathers help to provide optimal lift and minimal drag.
A bird's wing is curved along the top, a crucial aspect of its construction. As air passes over the leading edge of the wing, it divides, and because of the curve, the air on top must travel a greater distance before meeting the air that flowed across the bottom. The tendency of airflow, as noted earlier, is to correct for the presence of solid objects. Therefore, in the absence of outside factors such as viscosity, the air on top "tries" to travel over the wing in the same amount of time that it takes the air below to travel under the wing. As shown by Bernoulli, the fast-moving air above the wing exerts less pressure than the slow-moving air below it; hence there is a difference in pressure between the air below and the air above, and this keeps the wing aloft.
When a bird beats its wings, its downstrokes propel it, and as it rises above the ground, the force of aerodynamic lift helps push its wings upward in preparation for the next downstroke. However, to reduce aerodynamic drag during the upstroke, the bird folds its wings, thus decreasing its wingspan. Another trick that birds execute instinctively is the moving of their wings forward and backward in order to provide balance. They also "know" how to flap their wings in a direction almost parallel to the ground when they need to fly slowly or hover.
Witnessing the astonishing aerodynamic feats of birds, humans sought the elusive goal of flight from the earliest of times. This was symbolized by the Greek myth of Icarus and Daedalus, who escaped from a prison in Crete by constructing a set of bird-like wings and flying away. In the world of physical reality, however, the goal would turn out to be unattainable as long as humans attempted to achieve flight by imitating birds.
As noted earlier, a bird's physiology is quite different from that of a human being. There is simply no way that a human can fly by flapping his arms—nor will there ever be a man strong enough to do so, no matter how apparently well-designed his mechanical wings are. Indeed, to be capable of flying like a bird, a man would have to have a chest so enormous in proportion to his body that he would be hideous in appearance.
Not realizing this, humans for centuries attempted to fly like birds—with disastrous results. An English monk named Eilmer (b. 980) attempted to fly off the tower of Malmesbury Abbey with a set of wings attached to his arms and feet. Apparently Eilmer panicked after gliding some 600 ft (about 200 m) and suddenly plummeted to earth, breaking both of his legs. At least he lived; more tragic was the case of Abul Qasim Ibn Firnas (d. 873), an inventor from Cordoba in Arab Spain who devised and demonstrated a glider. Much of Cordoba's population came out to see him demonstrate his flying machine, but after covering just a short distance, the craft fell to earth. Severely wounded, Ibn Firnas died shortly afterward.
The first real progress in the development of flying machines came when designers stopped trying to imitate birds and instead used the principle of buoyancy. Hence in 1783, the French brothers Jacques-Etienne and Joseph-Michel Montgolfier constructed the first practical balloon.
Balloons and their twentieth-century descendant, the dirigible, had a number of obvious drawbacks, however. Without a motor, a balloon could not be guided, and even with a motor, dirigibles proved highly dangerous. At that stage, most dirigibles used hydrogen, a gas that is cheap and plentiful, but extremely flammable. After the Hindenburg exploded in 1937, the age of passenger travel aboard airships was over.
However, the German military continued to use dirigibles for observation purposes, as did the United States forces in World War II. Today airships, the most famous example being the Goodyear Blimp, are used not only for observation but for advertising. Scientists working in rain forests, for instance, use dirigibles to glide above the forest canopy; as for the Goodyear Blimp, it provides television networks with "eye in the sky" views of large sporting events.
The first man to make a serious attempt at creating a heavier-than-air flying machine (as opposed to a balloon, which uses gases that are lighter than air) was Sir George Cayley (1773-1857), who in 1853 constructed a glider. It is interesting to note that in creating this, the forerunner of the modern airplane, Cayley went back to an old model: the bird. After studying the physics of birds' flight for many years, he equipped his glider with an extremely wide wingspan, used the lightest possible materials in its construction, and designed it with exceptionally smooth surfaces to reduce drag.
The only thing that in principle differentiated Cayley's craft from a modern airplane was its lack of an engine. In those days, the only possible source of power was a steam engine, which would have added far too much weight to his aircraft. However, the development of the internal-combustion engine in the nineteenth century overcame that obstacle, and in 1903 Orville and Wilbur Wright achieved the dream of flight that had intrigued and eluded human beings for centuries.
Airplanes: Getting Aloft, Staying Aloft, and Remaining Stable
Once engineers and pilots took to the air, they encountered a number of factors that affect flight. In getting aloft and staying aloft, an aircraft is subject to weight, lift, drag, and thrust.
As noted earlier, the design of an airplane wing takes advantage of Bernoulli's principle to give it lift. Seen from the end, the wing has the shape of a long teardrop lying on its side, with the large end forward, in the direction of airflow, and the narrow tip pointing toward the rear. (Unlike a teardrop, however, an airplane's wing is asymmetrical, and the bottom side is flat.) This cross-section is known as an airfoil, and the greater curvature of its upper surface in comparison to the lower side is referred to as the airplane's camber. The front end of the airfoil is also curved, and the chord line is an imaginary straight line connecting the spot where the air hits the front—known as the stagnation point—to the rear, or trailing edge, of the wing.
Again in accordance with Bernoulli's principle, the shape of the airflow facilitates the spread of laminar flow around it. The slower-moving currents beneath the airfoil exert greater pressure than the faster currents above it, giving lift to the aircraft.
Another parameter influencing the lift coefficient (that is, the degree to which the aircraft experiences lift) is the size of the wing: the longer the wing, the greater the total force exerted beneath it, and the greater the ratio of this pressure to that of the air above. The size of a modern aircraft's wing is actually somewhat variable, due to the presence of flaps at the trailing edge.
With regard to the flaps, however, it should be noted that they have different properties at different stages of flight: in takeoff, they provide lift, but in stable flight they increase drag, and for that reason the pilot retracts them. In preparing for landing, as the aircraft slows and descends, the extended flaps then provide stability and assist in the decrease of speed.
Speed, too, encourages lift: the faster the craft, the faster the air moves over the wing. The pilot affects this by increasing or decreasing the power of the engine, thus regulating the speed with which the plane's propellers turn. Another highly significant component of lift is the airfoil's angle of attack—the orientation of the airfoil with regard to the air flow, or the angle that the chord line forms with the direction of the air stream.
Up to a point, increasing the angle of attack provides the aircraft with extra lift because it moves the stagnation point from the leading edge down along the lower surface; this increases the low-pressure area of the upper surface. However, if the pilot increases the angle of attack too much, this affects the boundary layer of slow-moving air, causing the aircraft to go into a stall.
Together the engine provides the propellers with power, and this gives the aircraft thrust, or propulsive force. In fact, the propeller blades constitute miniature wings, pivoted at the center and powered by the engine to provide rotational motion. As with the wings of the aircraft, the blades have a convex forward surface and a narrow trailing edge. Also like the aircraft wings, their angle of attack (or pitch) is adjusted at different points for differing effects. In stable flight, the pilot increases the angle of attack for the propeller blades sharply as against airflow, whereas at takeoff and landing the pitch is dramatically reduced. During landing, in fact, the pilot actually reverses the direction of the propeller blades, turning them into a brake on the aircraft's forward motion—and producing that lurching sensation that a passenger experiences as the aircraft slows after touching down.
By this point there have been several examples regarding the use of the same technique alternately to provide lift or—when slowing or preparing to land—drag. This apparent inconsistency results from the fact that the characteristics of air flow change drastically from situation to situation, and in fact, air never behaves as perfectly as it does in a textbook illustration of Bernoulli's principle.
Not only is the aircraft subject to air viscosity—the air's own friction with itself—it also experiences friction drag, which results from the fact that no solid can move through a fluid without experiencing a retarding force. An even greater drag factor, accounting for one-third of that which an aircraft experiences, is induced drag. The latter results because air does not flow in perfect laminar streams over the airfoil; rather, it forms turbulent eddies and currents that act against the forward movement of the plane.
In the air, an aircraft experiences forces that tend to destabilize flight in each of three dimensions. Pitch is the tendency to rotate forward or backward; yaw, the tendency to rotate on a horizontal plane; and roll, the tendency to rotate vertically on the axis of its fuselage. Obviously, each of these is a terrifying prospect, but fortunately, pilots have a solution for each. To prevent pitching, they adjust the angle of attack of the horizontal tail at the rear of the craft. The vertical rear tail plays a part in preventing yawing, and to prevent rolling, the pilot raises the tips of the main wings so that the craft assumes a V-shape when seen from the front or back.
The above factors of lift, drag, thrust, and weight, as well as the three types of possible destabilization, affect all forms of heavier-thanair flying machines. But since the 1944 advent of jet engines, which travel much faster than piston-driven engines, planes have flown faster and faster, and today some craft such as the Concorde are capable of supersonic flight. In these situations, air compressibility becomes a significant issue.
Sound is transmitted by the successive compression and expansion of air. But when a plane is traveling at above Mach 1.2—the Mach number indicates the speed of an aircraft in relation to the speed of sound—there is a significant discrepancy between the speed at which sound is traveling away from the craft, and the speed at which the craft is moving away from the sound. Eventually the compressed sound waves build up, resulting in a shock wave.
Down on the ground, the shock wave manifests as a "sonic boom"; meanwhile, for the aircraft, it can cause sudden changes in pressure, density, and temperature, as well as an increase in drag and a loss of stability. To counteract this effect, designers of supersonic and hypersonic (Mach 5 and above) aircraft are altering wing design, using a much narrower airfoil and swept-back wings.
One of the pioneers in this area is Richard Whitcomb of the National Aeronautics and Space Administration (NASA). Whitcomb has designed a supercritical airfoil for a proposed hypersonic plane, which would ascend into outer space in the course of a two-hour flight—all the time needed for it to travel from Washington, D.C., to Tokyo, Japan. Before the craft can become operational, however, researchers will have to figure out ways to control temperatures and keep the plane from bursting into flame as it reenters the atmosphere.
Much of the research for improving the aerodynamic qualities of such aircraft takes place in wind tunnels. First developed in 1871, these use powerful fans to create strong air currents, and over the years the top speed in wind tunnels has been increased to accommodate testing on supersonic and hypersonic aircraft. Researchers today use helium to create wind blasts at speeds up to Mach 50.
Thrown and Flown: The Aerodynamics of Small Objects
Long before engineers began to dream of sending planes into space for transoceanic flight—about 14,000 years ago, in fact—many of the features that make an airplane fly were already present in the boomerang. It might seem backward to move from a hypersonic jet to a boomerang, but in fact, it is easier to appreciate the aerodynamics of small objects, including the kite and even the paper airplane, once one comprehends the larger picture.
There is a certain delicious irony in the fact that the first manmade object to take flight was constructed by people who never advanced beyond the Stone Age until the nineteenth century, when the Europeans arrived in Australia. As the ethnobotanist Jared Diamond showed in his groundbreaking work Guns, Germs, and Steel: The Fates of Human Societies (1997), this was not because the Aborigines of Australia were less intelligent than Europeans. In fact, as Diamond showed, an individual would actually have to be smarter to figure out how to survive on the limited range of plants and animals available in Australia prior to the introduction of Eurasian flora and fauna. Hence the wonder of the boomerang, one of the most ingenious inventions ever fashioned by humans in a "primitive" state.
Thousands of years before Bernoulli, the boomerang's designers created an airfoil consistent with Bernoulli's principle. The air below exerts more pressure than the air above, and this, combined with the factors of gyroscopic stability and gyroscopic precession, gives the boomerang flight.
Gyroscopic stability can be illustrated by spinning a top: the action of spinning itself keeps the top stable. Gyroscopic precession is a much more complex process: simply put, the leading wing of the boomerang—the forward or upward edge as it spins through the air—creates more lift than the other wing. At this point it should be noted that, contrary to the popular image, a boomerang travels on a plane perpendicular to that of the ground, not parallel. Hence any thrower who knows what he or she is doing tosses the boomerang not with a side-arm throw, but overhand.
And of course a boomerang does not just sail through the air; a skilled thrower can make it come back as if by magic. This is because the force of the increased lift that it experiences in flight, combined with gyroscopic precession, turns it around. As noted earlier, in different situations the same force that creates lift can create drag, and as the boomerang spins downward the increasing drag slows it. Certainly it takes great skill for a thrower to make a boomerang come back, and for this reason, participants in boomerang competitions often attach devices such as flaps to increase drag on the return cycle.
Another very early example of an aerodynamically sophisticated humanmade device—though it is quite recent compared to the boomerang—is the kite, which first appeared in China in about 1000 b.c. The kite's design borrows from avian anatomy, particularly the bird's light, hollow bones. Hence a kite, in its simplest form, consists of two crossed strips of very light wood such as balsa, with a lightweight fabric stretched over them.
Kites can come in a variety of shapes, though for many years the well-known diamond shape has been the most popular, in part because its aerodynamic qualities make it easiest for the novice kite-flyer to handle. Like birds and boomerangs, kites can "fly" because of the physical laws embodied in Bernoulli's principle: at the best possible angle of attack, the kite experiences a maximal ratio of pressure from the slower-moving air below as against the faster-moving air above.
For centuries, when the kite represented the only way to put a humanmade object many hundreds of feet into the air, scientists and engineers used them for a variety of experiments. Of course, the most famous example of this was Benjamin Franklin's 1752 experiment with electricity. More significant to the future of aerodynamics were investigations made half a century later by Cayley, who recognized that the kite, rather than the balloon, was an appropriate model for the type of heavier-than-air flight he intended.
In later years, engineers built larger kites capable of lifting men into the air, but the advent of the airplane rendered kites obsolete for this purpose. However, in the 1950s an American engineer named Francis Rogallo invented the flexible kite, which in turn spawned the delta wing kite used by hang gliders. During the 1960s, Domina Jolbert created the parafoil, an even more efficient device, which took nonmechanized human flight perhaps as far as it can go.
Akin to the kite, glider, and hang glider is that creation of childhood fancy, the paper airplane. In its most basic form—and paper airplane enthusiasts are capable of fairly complex designs—a paper airplane is little more than a set of wings. There are a number or reasons for this, not least the fact that in most cases, a person flying a paper airplane is not as concerned about pitch, yaw, and roll as a pilot flying with several hundred passengers on board would be.
However, when fashioning a paper airplane it is possible to add a number of design features, for instance by folding flaps upward at the tail. These become the equivalent of the elevator, a control surface along the horizontal edge of a real aircraft's tail, which the pilot rotates upward to provide stability. But as noted by Ken Blackburn, author of several books on paper airplanes, it is not necessarily the case that an airplane must have a tail; indeed, some of the most sophisticated craft in the sky today—including the fearsome B-2 "Stealth" bomber—do not have tails.
A typical paper airplane has low aspect ratio wings, a term that refers to the size of the wingspan compared to the chord line. In subsonic flight, higher aspect ratios are usually preferred, and this is certainly the case with most "real" gliders; hence their wings are longer, and their chord lines shorter. But there are several reasons why this is not the case with a paper airplane.
First of all, as Blackburn noted wryly on his Web site, "Paper is a lousy building material. There is a reason why real airplanes are not made of paper." He stated the other factors governing paper airplanes' low aspect ratio in similarly whimsical terms. First, "Low aspect ratio wings are easier to fold…."; second, "Paper airplane gliding performance is not usually very important…."; and third, "Low-aspect ratio wings look faster, especially if they are swept back."
The reason why low-aspect ratio wings look faster, Blackburn suggested, is that people see them on jet fighters and the Concorde, and assume that a relatively narrow wing span with a long chord line yields the fastest speeds. And indeed they do—but only at supersonic speeds. Below the speed of sound, high-aspect ratio wings are best for preventing drag. Furthermore, as Blackburn went on to note, low-aspect ratio wings help the paper airplane to with stand the relatively high launch speeds necessary to send them into longer glides.
In fact, a paper airplane is not subject to anything like the sort of design constraints affecting a real craft. All real planes look somewhat similar, because the established combinations, ratios, and dimensions of wings, tails, and fuselage work best. Certainly there is a difference in basic appearance between subsonic and supersonic aircraft—but again, all supersonic jets have more or less the same low-aspect, swept wing. "With paper airplanes," Blackburn wrote, "it's easy to make airplanes that don't look like real airplanes" since "The mission of a paper airplane is [simply] to provide a good time for the pilot."
Aerodynamics on the Ground
The preceding discussions of aerodynamics in action have concerned the behavior of objects off the ground. But aerodynamics is also a factor in wheeled transport on Earth's surface, whether by bicycle, automobile, or some other variation.
On a bicycle, the rider accounts for 65-80% of the drag, and therefore his or her position with regard to airflow is highly important. Thus, from as early as the 1890s, designers of racing bikes have favored drop handlebars, as well as a seat and frame that allow a crouched position. Since the 1980s, bicycle designers have worked to eliminate all possible extra lines and barriers to airflow, including the crossbar and chainstays.
A typical bicycle's wheel contains 32 or 36 cylindrical spokes, and these can affect aerodynamics adversely. As the wheel rotates, the airflow behind the spoke separates, creating turbulence and hence drag. For this reason, some of the most advanced bicycles today use either aerodynamic rims, which reduce the length of the spokes, three-spoke aerodynamic wheels, or even solid wheels.
The rider's gear can also serve to impede or enhance his velocity, and thus modern racing helmets have a streamlined shape—rather like that of an airfoil. The best riders, such as those who compete in the Olympics or the Tour de France, have bikes custom-designed to fit their own body shape.
One interesting aspect of aerodynamics where it concerns bicycle racing is the phenomenon of "drafting." Riders at the front of a pack, like riders pedaling alone, consume 30-40% more energy than do riders in the middle of a pack. The latter are benefiting from the efforts of bicyclists in front of them, who put up most of the wind resistance. The same is true for bicyclists who ride behind automobiles or motorcycles.
The use of machine-powered pace vehicles to help in achieving extraordinary speeds is far from new. Drafting off of a railroad car with specially designed aerodynamic shields, a rider in 1896 was able to exceed 60 MPH (96 km/h), a then unheard-of speed. Today the record is just under 167 MPH (267 km/h). Clearly one must be a highly skilled, powerful rider to approach anything like this speed; but design factors also come into play, and not just in the case of the pace vehicle. Just as supersonic jets are quite different from ordinary planes, super high-speed bicycles are not like the average bike; they are designed in such a way that they must be moving faster than 60 MPH before the rider can even pedal.
With regard to automobiles, as noted earlier, aerodynamics has a strong impact on body design. For this reason, cars over the years have become steadily more streamlined and aerodynamic in appearance, a factor that designers balance with aesthetic appeal. Today's Chrysler PT Cruiser, which debuted in 2000, may share outward features with 1930s and 1940s cars, but the PT Cruiser's design is much more sound aerodynamically—not least because a modern vehicle can travel much, much faster than the cars driven by previous generations.
Nowhere does the connection between aerodynamics and automobiles become more crucial than in the sport of auto racing. For race-car drivers, drag is always a factor to be avoided and counteracted by means ranging from drafting to altering the body design to reduce the airflow under the vehicle. However, as strange as it may seem, a car—like an airplane—is also subject to lift.
It was noted earlier that in some cases lift can be undesirable in an airplane (for instance, when trying to land), but it is virtually always undesirable in an automobile. The greater the speed, the greater the lift force, which increases the threat of instability. For this reason, builders of race cars design their vehicles for negative lift: hence a typical family car has a lift coefficient of about 0.03, whereas a race car is likely to have a coefficient of −3.00.
Among the design features most often used to reduce drag while achieving negative lift is a rear-deck spoiler. The latter has an airfoil shape, but its purpose is different: to raise the rear stagnation point and direct air flow so that it does not wrap around the vehicle's rear end. Instead, the spoiler creates a downward force to stabilize the rear, and it may help to decrease drag by reducing the separation of airflow (and hence the creation of turbulence) at the rear window.
Similar in concept to a spoiler, though somewhat different in purpose, is the aerodynamically curved shield that sits atop the cab of most modern eighteen-wheel transport trucks. The purpose of the shield becomes apparent when the truck is moving at high speeds: wind resistance becomes strong, and if the wind were to hit the truck's trailer head-on, it would be as though the air were pounding a brick wall. Instead, the shield scoops air upward, toward the rear of the truck. At the rear may be another panel, patented by two young engineers in 1994, that creates a drag-reducing vortex between panel and truck.
WHERE TO LEARN MORE
Cockpit Physics (Department of Physics, United States Air Force Academy web site.). <http://www.usafa.af.mil/dfp/cockpit-phys/> (February 19, 2001).
K8AIT Principles of Aeronautics Advanced Text. (web site). <http://wings.ucdavis.edu/Book/advanced.html> (February 19, 2001).
Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998.
Blackburn, Ken. Paper Airplane Aerodynamics. (web site). <http://www.geocities.com/CapeCanaveral/1817/paero.html> (February 19, 2001).
Schrier, Eric and William F. Allman. Newton at the Bat: The Science in Sports. New York: Charles Scribner's Sons, 1984.
Smith, H. C. The Illustrated Guide to Aerodynamics. Blue Ridge Summit, PA: Tab Books, 1992.
Stever, H. Guyford, James J. Haggerty, and the Editors of Time-Life Books. Flight. New York: Time-Life Books, 1965.
Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
The study of airflow and its principles. Applied aerodynamics is the science of improving man-made objects in light of those principles.
The design of an airplane's wing when seen from the end, a shape intended to maximize the aircraft's response to airflow.
ANGLE OF ATTACK:
The orientation of the airfoil with regard to the airflow, or the angle that the chord line forms with the direction of the air stream.
A proposition, credited to Swiss mathematician and physicist Daniel Bernoulli (1700-1782), which maintains that slower-moving fluid exerts greater pressure than faster-movingfluid.
The enhanced curvature on the upper surface of an airfoil.
The distance, along an imaginary straight line, from the stagnation point of an airfoil to the rear, or trailing edge.
The force that opposes the forward motion of an object in airflow.
A term describing a streamlined flow, in which all particles move at the same speed and in the same direction. Its opposite is turbulent flow.
An aerodynamic force perpendicular to the direction of the wind. For an aircraft, lift is the force that raises it off the ground and keeps it aloft.
The tendency of an aircraft in flight to rotate forward or backward; see also yaw and roll.
The tendency of an aircraft in flight to rotate vertically on the axis of its fuselage; see also pitch and yaw.
The spot where airflow hits the leading edge of an airfoil.
Faster than Mach 1, or the speed of sound—660 MPH (1,622km/h). Speeds above Mach 5 are referred to as hypersonic.
A term describing a highly irregular form of flow, in which a fluid is subject to continual changes in speed and direction. Its opposite is laminar flow.
The internal friction in a fluid that makes it resistant to flow.
The tendency of an aircraft in flight to rotate on a horizontal plane; see also Pitch and Roll.
"Aerodynamics." Science of Everyday Things. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/science/news-wires-white-papers-and-books/aerodynamics
"Aerodynamics." Science of Everyday Things. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/news-wires-white-papers-and-books/aerodynamics
Aerodynamics is the science of airflow over airplanes, cars, buildings, and other objects. Aerodynamic principles are used to find the best ways in which airplanes produce lift, reduce drag, and remain stable (by controlling the shape and size of the wing, the angle at which it is positioned with respect to the airstream, and the flight speed). The flight characteristics change at higher altitudes as the surrounding air becomes colder and thinner. The behavior of the airflow also changes dramatically at flight speeds close to, and beyond, the speed of sound. The explosion in computational capability has made it possible to understand and exploit the concepts of aerodynamics and to design improved wings for airplanes. Increasingly sophisticated wind tunnels are also available to test new models.
Airflow is governed by the principles of fluid dynamics that deal with the motion of liquids and gases in and around solid surfaces. The viscosity, density, compressibility, and temperature of the air determine how the air will flow around a building or a plane. The viscosity of a fluid is its resistance to flow. Even though air is 55 times less viscous than water , viscosity is important near a solid surface because air, like all other fluids, tends to stick to the surface and slow down the flow. A fluid is compressible if its density can be increased by squeezing it into a smaller volume. At flow speeds less than 220 mph (354 kph), one third the speed of sound, we can assume that air is incompressible for all practical purposes. At speeds closer to that of sound (660 mph [1,622 kph]) however, the variation in the density of the air must be taken into account. The effects of temperature change also become important at these speeds. A regular commercial airplane, after landing, will feel cool to the touch. The Concorde jet, which flies at twice the speed of sound, can feel hotter than boiling water.
Flow patterns of the air may be laminar or turbulent. In laminar or streamlined flow, air, at any point in the flow, moves with the same speed in the same direction at all times so that smoke in the flow appears to be smooth and regular. The smoke then changes to turbulent flow, which is cloudy and irregular, with the air continually changing speed and direction.
Laminar flow, without viscosity, is governed by Bernoulli's principle that states that the sum of the static and dynamic pressures in a fluid remains the same. A fluid at rest in a pipe exerts static pressure on the walls. If the fluid starts moving, some of the static pressure is converted to dynamic pressure, which is proportional to the square of the speed of the fluid. The faster a fluid moves, the greater its dynamic pressure and the smaller the static pressure it exerts on the sides.
Bernoulli's principle works very well far from the surface. Near the surface, however, the effects of viscosity must be considered since the air tends to stick to the surface, slowing down the flow nearby. Thus, a boundary layer of slow-moving air is formed on the surface of an airplane or automobile. This boundary layer is laminar at the beginning of the flow, but it gets thicker as the air moves along the surface and becomes turbulent after a point.
Airflow is determined by many factors, all of which work together in complicated ways to influence flow. Very often, the effects of factors such as viscosity, speed, and turbulence cannot be separated. Engineers have found ingenious ways to get around the difficulty of treating such complex situations. They have defined some characteristic numbers, each of which tells us something useful about the nature of the flow by taking several different factors into account.
One such number is the Reynolds number, which is greater for faster flows and denser fluids and smaller for more viscous fluids. The Reynolds number is also higher for flow around larger objects. Flows at lower Reynolds numbers tend to be slow, viscous, and laminar. As the Reynolds number increases, there is a transition from laminar to turbulent flow. The Reynolds number is a useful similarity parameter. This means that flows in completely different situations will behave in the same way as long as the Reynolds number and the shape of the solid surface are the same. If the Reynolds number is kept the same, water moving around a small stationary airplane model will create exactly the same flow patterns as a full-scale airplane of the same shape, flying through the air. This principle makes it possible to test airplane and automobile designs using small-scale models in wind tunnels.
At speeds greater than 220 mph (354 kph), the compressibility of air cannot be ignored. At these speeds, two different flows may not be equivalent even if they have the same Reynolds number. Another similarity parameter, the Mach number, is needed to make them similar. The Mach number of an airplane is its flight speed divided by the speed of sound at the same altitude and temperature. This means that a plane flying at the speed of sound has a Mach number of one.
The drag coefficient and the lift coefficient are two numbers that are used to compare the forces in different flow situations. Aerodynamic drag is the force that opposes the motion of a car or an airplane. Lift is the upward force that keeps an airplane afloat against gravity . The drag or lift coefficient is defined as the drag or lift force divided by the dynamic pressure, and also by the area over which the force acts. Two objects with similar drag or lift coefficients experience comparable forces, even when the actual values of the drag or lift force, dynamic pressure, area, and shape are different in the two cases.
There are several sources of drag. The air that sticks to the surface of a car creates a drag force due to skin friction. Pressure drag is created when the shape of the surface changes abruptly, as at the point where the roof of an automobile ends. The drop from the roof increases the space through which the air stream flows. This slows down the flow and, by Bernoulli's principle, increases the static pressure. The air stream is unable to flow against this sudden increase in pressure and the boundary layer gets detached from the surface creating an area of low-pressure turbulent wake or flow. Because the pressure in the wake is much lower than the pressure in front of the car, a net backward drag or force is exerted on the car. Pressure drag is the major source of drag on blunt bodies. Car manufacturers experiment with vehicle shapes to minimize the drag. For smooth or "streamlined" shapes, the boundary layer remains attached longer, producing only a small wake. For such bodies, skin friction is the major source of drag, especially if they have large surface areas. Skin friction comprises almost 60% of the drag on a modern airliner.
An airfoil is the two-dimensional cross-section of the wing of an airplane as one looks at it from the side. It is designed to maximize lift and minimize drag. The upper surface of a typical airfoil has a curvature greater than that of the lower surface. This extra curvature is known as camber. The straight line, joining the front tip or the leading edge of the airfoil to the rear tip or the trailing edge, is known as the chord line. The angle of attack is the angle that the chord line forms with the direction of the air stream.
The stagnation point is the point at which the stream of air moving toward the wing divides into two streams, one flowing above and the other flowing below the wing. Air flows faster above a wing with greater camber since the same amount of air has to flow through a narrower space. According to Bernoulli's principle, the faster flowing air exerts less pressure on the top surface, so that the pressure on the lower surface is higher, and there is a net upward force on the wing, creating lift. The camber is varied, using flaps and slats on the wing in order to achieve different degrees of lift during takeoff, cruise, and landing.
Because the air flows at different speeds above and below the wing, a large jump in speed will tend to arise when the two flows meet at the trailing edge, leading to a rearward stagnation point on top of the wing. Wilhelm Kutta (1867–1944) discovered that a circulation of air around the wing would ensure smooth flow at the trailing edge. According to the Kutta condition, the strength of the circulation, or the speed of the air around the wing, is exactly as much as is needed to keep the flow smooth at the trailing edge.
Increasing the angle of attack moves the stagnation point down from the leading edge along the lower surface so that the effective area of the upper surface is increased. This results in a higher lift force on the wing. If the angle is increased too much, however, the boundary layer is detached from the surface, causing a sudden loss of lift. This is known as a stall; the angle at which this occurs for an airfoil of a particular shape is known as the stall angle.
The airfoil is a two-dimensional section of the wing. The length of the wing in the third dimension, out to the side, is known as the span of the wing. At the wing tip at the end of the span, the high-pressure flow below the wing meets the low-pressure flow above the wing, causing air to move up and around in wing-tip vortices. These vortices are shed as the plane moves forward, creating a downward force or down-wash behind it. The downwash makes the airstream tilt downward and the resulting lift force tilt backward so that a net backward force or drag is created on the wing. This is known as induced drag or drag due to lift. About one third of the drag on a modern airliner is induced drag.
In addition to lift and drag, the stability and control of an aircraft in all three dimensions is important since an aircraft, unlike a car, is completely surrounded by air. Various control devices on the tail and wing are used to achieve this. Ailerons, for instance, control rolling motion by increasing lift on one wing and decreasing lift on the other.
Flight at speeds greater than that of sound are supersonic. Near a Mach number of one, some portions of the flow are at speeds below that of sound, while other portions move faster than sound. The range of speeds from Mach number 0.8 to 1.2 is known as transonic. Flight at Mach numbers greater than five is hypersonic.
The compressibility of air becomes an important aerodynamic factor at these high speeds. The reason for this is that sound waves are transmitted through the successive compression and expansion of air. The compression due to a sound wave from a supersonic aircraft does not have a chance to get away before the next compression begins. This pile up of compression creates a shock wave, which is an abrupt change in pressure, density, and temperature. The shock wave causes a steep increase in the drag and loss of stability of the aircraft. Drag due to the shock wave is known as wave drag. The familiar "sonic boom" is heard when the shock wave touches the surface of the earth.
Temperature effects also become important at transonic speeds. At hypersonic speeds above a Mach number of five, the heat causes nitrogen and oxygen molecules in the air to break up into atoms and form new compounds by chemical reactions. This changes the behavior of the air and the simple laws relating pressure, density, and temperature become invalid.
The need to overcome the effects of shock waves has been a formidable problem. Swept-back wings have helped to reduce the effects of shock. The supersonic Concorde that cruises at Mach 2 and several military airplanes have delta or triangular wings. The supercritical airfoil designed by Richard Whitcomb of the NASA Langley Laboratory has made air flow around the wing much smoother and has greatly improved both the lift and drag at transonic speeds. It has only a slight curvature at the top and a thin trailing edge. The proposed hypersonic aerospace plane is expected to fly partly in air and partly in space and to travel from Washington to Tokyo within two hours. The challenge for aerodynamicists is to control the flight of the aircraft so that it does not burn up like a meteor as it returns to Earth at several times the speed of sound.
See also Atmosphere; Atmospheric circulation; Atmospheric composition and structure; Atmospheric pressure; Aviation physiology; Bernoulli's equation; Meteorology; Physics; Space physiology; Wind shear
"Aerodynamics." World of Earth Science. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/aerodynamics
"Aerodynamics." World of Earth Science. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/aerodynamics
Aerodynamics is the study of air flow over airplanes, cars, and other objects. Airplanes fly because of the way in which air flows over their wings and around their bodies, so a knowledge of aerodynamics is crucial to the design and construction of airplanes. The efficiency with which automobiles use fuel is also a function of air flow. Even stationary objects are affected by aerodynamics. Winds blowing past a tall building, for example, may cause windows to pop out if they are not properly designed and installed.
Factors affecting air flow
Four properties of air affect the way in which it flows past an object: viscosity, density, compressibility, and temperature. Viscosity is the resistance of a fluid to flow. Molasses is very viscous because is flows slowly, while water is less viscous because it flows readily. The viscosity of air is important in aerodynamics because air tends to stick to any surface over which it flows, slowing down the motion of the air.
The density and compressibility of air are important factors at high speeds. As an object travels rapidly through air, it causes air to become compressed and more dense. As a result, other properties of air then change.
The effects of temperature change on air flow also become important at high speeds. A regular commercial airplane, after landing, will feel cool to the touch. But the Concorde jet, which flies at twice the speed of sound, will feel hotter than boiling water.
Laminar and turbulent flow
Air can travel over a surface following patterns of flow referred to as either laminar or turbulent. In laminar or streamlined flow, air moves with the same speed in the same direction at all times. The flow appears to be smooth and regular. Bernoulli's principle applies during laminar flow. Bernoulli's principle states that a fluid (such as air) traveling over the surface of an object exerts less pressure than if the fluid were still. Airplanes fly because of Bernoulli's principle. When an airplane takes off, air rushes over the top surface of its wing, reducing pressure on the upper surface of the wing. Normal pressure below the wing pushes the wing upward, carrying the airplane upward along with it.
Turbulent flow is chaotic and unpredictable. It consists of irregular eddies (circular currents) of air that push on a surface in unexpected ways. The bumpy ride you may have experienced on a commercial airplane could have resulted from the development of turbulent flow over the airplane's wings.
Skin friction and pressure drag
Drag is any force that tends to prevent an object from moving forward. One source of drag in airplanes and automobiles is skin friction. As air passes over the surface of either vehicle, friction between air and surface tends to slow the plane or automobile down. One of the goals of transportation engineers is to find a shape that has the least amount of skin friction, thus reducing the amount of drag on the vehicle. Sleek, tear-drop-shaped cars became popular in the middle to late 1990s because they had so little skin friction.
Engineers also work to reduce pressure drag. Pressure drag is caused by abrupt changes in the shape of a car or airplane. The point at which the roof of a car ends, as an example, is a point of high pressure drag. A car designed with a smooth transition from roof to trunk will have less pressure drag and, therefore, will travel more smoothly.
Words to Know
Airfoil: The cross section of an airplane wing parallel to (or running in the same direction as) the length of the plane.
Angle of attack: The angle that the length of the airfoil forms with an oncoming airstream.
Camber: The additional curvature of the upper surface of the airfoil relative to the lower surface.
Induced drag: Also known as drag due to lift; the drag on the airplane due to vortices (whirling patterns of air) on the wingtips.
Stall: A sudden loss of lift on the airplane wing when the angle of attack increases beyond a certain value.
Supersonic speed: A speed greater than that of sound.
An airfoil is a two-dimensional cross section of the wing of an airplane as viewed from the side. Engineers seek to design airfoils that will have the greatest amount of lift and the least amount of drag. One factor important in the design of an airfoil is the curvature, or camber, of the upper side of the wing. The greater the camber, the faster air moves over the upper surface and the greater the lift to the wing. The amount of camber in a wing is changed by means of flaps and slats in the wing that produce different amounts of lift during take-off, cruise, and landing.
Another factor affecting lift is the angle of attack: the position of the wing in comparison to the ground. As the forward edge of the wing is tipped downward, the amount of lift on the wing is increased. Increasing the angle of attack too much, however, may result in a sudden loss of lift, causing the airplane to lose all lift and go into a stall.
Air movement around an airplane wing can also cause drag effects. At the very tip of the wing, air traveling above and below the wing meet and produce whirlpool-like patterns known as vortices. These vortices tend to pull the wing downward, thus producing drag forces on the wing. These forces are known as induced drag.
What do jet airplanes and a baseball pitcher's curveball have in common? They both depend on Bernoulli's principle for their operation. Bernoulli's principle states that the faster a fluid (such as air or water) flows over a surface, the less pressure the fluid exerts on that surface.
In the case of the jet airplane, air travels faster over the top of the wing than across the bottom of the wing. Since the pressure on top of the wing is reduced, the airplane is pushed upward. A pitcher can cause a baseball to curve by making it spin. On one side of the ball, air carried along by the spinning ball rushes past in the same direction the ball is traveling. On the other side of the ball, air is pushed in the opposite direction. On the side of the ball where air is traveling faster, pressure is reduced. Higher air pressure on the opposite side of the ball pushes it out of a straight path, causing it to curve.
Stability and control
Aerodynamics is applied to other problems of air flight as well. Airplanes have tendencies to rotate in one of three directions: in a horizontal back-and-forth motion around the center of the airplane, in a front-over-back motion, or in a rolling fashion, wing-over-wing. Special controls must be developed to prevent loss of control in any of these directions, any one of which could cause the airplane to crash. Ailerons (pronounced AYL-uh-ronz) are one such control. They prevent a rolling action by increasing the lift on one wing while decreasing it on the other.
Flight at speeds greater than that of sound present special problems for engineers. One reason is the importance of the compressibility of air at these speeds. Sound waves produced by an aircraft moving through the air travel more slowly than the aircraft itself. This produces a shock wave characterized by an abrupt change in temperature, pressure, and density that causes a steep increase in the drag and loss of stability of the aircraft. The loud sonic boom one hears is the wave hitting Earth's surface.
The need to overcome the effects of shock waves has been a major problem for engineers. Swept-back wings are one way of reducing the effects of shock. The delta or triangular wings of the supersonic Concorde and several military airplanes are another solution. The most advanced airplane designs actually call for the complete retraction of the wings during the fastest part of a flight, converting them into a rocket for part of the trip.
[See also Aircraft; Balloon; Fluid dynamics ]
"Aerodynamics." UXL Encyclopedia of Science. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/aerodynamics-2
"Aerodynamics." UXL Encyclopedia of Science. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/encyclopedias-almanacs-transcripts-and-maps/aerodynamics-2
aerodynamics, study of gases in motion. As the principal application of aerodynamics is the design of aircraft, air is the gas with which the science is most concerned. Although aerodynamics is primarily concerned with flight, its principles are also used in designing automobile and train bodies for minimum drag and in computing wind stresses on bridges, buildings, smokestacks, trees, and other structures. It is also used in charting flows of pollutants in the atmosphere and in determining frictional effects in gas ducts. The wind tunnel is one of the aerodynamicist's basic experimental tools; however in recent years, it has been supplanted by the simulation of aerodynamic forces during the computer-aided design of aircraft and automobiles.
The Basic Forces of Thrust, Drag, and Lift
There are three basic forces to be considered in aerodynamics: thrust, which moves an airplane forward; drag, which holds it back; and lift, which keeps it airborne. Lift is generally explained by three theories: Bernoulli's principle, the Coanda effect, and Newton's third law of motion. Bernoulli's principle states that the pressure of a moving gas decreases as its velocity increases. When air flows over a wing having a curved upper surface and a flat lower surface, the flow is faster across the curved surface than across the plane one; thus a greater pressure is exerted in the upward direction. This principle, however, does not fully explain flight; for example, it does not explain how an airplane can fly upside down. Scientists have begun suggesting that the Coanda effect is at least partially responsible for how planes fly. Regardless of the shape of a plane's wing, the Coanda effect, in which moving air is attracted to and flows along the surface of the wing, and the tilt of the wing, called the angle of attack, cause the air to flow downward as it leaves the wing. The greater the angle of attack, the greater the downward flow. In obedience to Newton's third law of motion, which requires an equal and opposite reaction, the airplane is deflected upward. At the same time, a force that retards the forward motion of the aircraft is developed by diverting air in this way and is known as drag due to lift. Another kind of drag is caused by the slowing of air very near to the aircraft's surface; this can be reduced by making the surface area of the craft as small as possible. At low speeds (below Mach .7) the ratio between lift and drag decreases with gains in speed; accordingly, aerodynamic development for many years stressed increases in thrust over real reductions in drag.
Creation of Shock Waves
Above speeds of Mach .7 the air flowing over the wing accelerates above the speed of sound, causing a shock wave (also known as a sonic boom) as the airplane compresses air molecules faster than they can move away from the airplane. The danger of this shock wave is its effect on control surfaces and fragile wing members, and for many years it was thought to represent a near-solid barrier to faster flight. The problems associated with this shock wave were ultimately conquered through the use of swept-back wings and the moving of critical control surfaces out of the wave's direct path. Chuck Yeager, in 1947, was the first to fly at sustained supersonic speed. Other troublesome phenomena associated with supersonic flight are the shock waves that build up at engine air intakes, and the much larger wave that trails after the craft.
Effect of Hypersonic Speeds
Recently, intense research has gone into the development of planes that can fly at hypersonic speeds, approximately five times or more than the speed of sound. At these speeds the properties of air change radically; there is a rapid increase in temperature associated with the air flowing at such speeds along a plane's surface. The U.S. Air Force is working to develop an aircraft that could travel at 13,000 mph (21,000 kph), a speed that would generate temperatures greater than 3,500°F (2,000°C).
See A. M. Kuethe and C. Y. Chow, Foundations of Aerodynamics (5th ed. 1997); D. Anderson and S. Eberhardt, Understanding Flight (2001); G. Craig, Introduction to Aerodynamics (2003); D. Bloor, The Enigma of the Aerofoil: Rival Theories in Aerodynamics, 1909–1930 (2011).
"aerodynamics." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/aerodynamics
"aerodynamics." The Columbia Encyclopedia, 6th ed.. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/aerodynamics
aer·o·dy·nam·ics / ˌe(ə)rōdīˈnamiks/ • pl. n. [treated as sing.] the study of the properties of moving air, and esp. of the interaction between the air and solid bodies moving through it. ∎ the properties of a solid object regarding the manner in which air flows around it. ∎ [treated as pl.] these properties insofar as they result in maximum efficiency of motion. DERIVATIVES: aer·o·dy·nam·i·cist / -ˈnaməsist/ n.
"aerodynamics." The Oxford Pocket Dictionary of Current English. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/aerodynamics
"aerodynamics." The Oxford Pocket Dictionary of Current English. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/humanities/dictionaries-thesauruses-pictures-and-press-releases/aerodynamics
"aerodynamics." World Encyclopedia. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/aerodynamics
"aerodynamics." World Encyclopedia. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/aerodynamics