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Drag (physics)

Drag (physics)

:This page is about forces which tend to slow a moving object. For other uses, see Drag (disambiguation). For a solid object moving through a fluid or gas, drag is the sum of all the aerodynamic or hydrodynamic forces in the direction of the external fluid flow. It therefore acts to oppose the motion of the object, and in a powered vehicle it is overcome by thrust. Types of drag are generally divided into three categories: parasitic drag, lift-induced drag and wave drag. Parasitic drag includes form drag, skin friction and interference drag. Lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed only in the aviation perspective of drag. Beyond these two kinds of drag there is a third kind of drag, called wave drag, that occurs when the solid object is moving through the fluid at or near the speed of sound in that fluid. 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 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 density, the cross sectional area of your 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 (disambiguation)

Drag may mean:
- drag (physics), a combination of aerodynamic or hydrodynamic forces which tends to reduce speed
- Drag (clothing), slang for any costume, but particularly for clothes of one gender worn by the opposite gender
- Drag racing, a form of automobile racing
- Drag (film), a 1929 film

Fluid

A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. Fluids share the properties of not resisting deformation and the ability to flow (also described as their ability to take on the shape of their containers). These properties are typically a function of their inability to support a shear stress in static equilibrium. While in a solid, stress is a function of strain, in a fluid stress is a function of rate of strain. A consequence of this behaviour is Pascal's law which entails the important role of pressure in characterising a fluid's state. Fluids can be characterised as:
- Newtonian fluids; or
- Non-Newtonian fluids, - depending on the way stress depends on strain and its derivatives. The behaviour of fluids is described by a set of partial differential equations, including the Navier-Stokes equations. Fluids are also divided into liquids and gases. Liquids form a free surface (that is, a surface not created by their container) while gases do not. The distinction between solids and fluids is not so obvious. The distinction is made by evaluating the viscosity of the matter: for example Silly Putty can be considered either a solid or a fluid, depending on the time period over which it is observed. The study of fluids is fluid mechanics which is then subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion or not.

Gas

:For other meanings see gas (disambiguation). ---- A gas is one of the four main phases of matter (after solid and liquid, and followed by plasma), that subsequently appear as a solid material is subjected to increasingly higher temperatures. Thus, as energy in the form of heat is added, a solid (e.g. ice) will first melt to become a liquid (e.g. water), which will then boil or evaporate to become a gas (e.g. water vapor). In some circumstances, a solid (e.g. "dry ice") can directly turn into a gas: this is called sublimation. If the gas is further heated, its atoms or molecules can become (wholly or partially) ionized, turning the gas into a plasma.

Properties of a gas

#All collisions are perfectly elastic #The gas fills the entire container #The molecules have negligible volume In the gas phase, the atoms or molecules constituting the matter basically move independently, with no forces keeping them together or pushing them apart. Their only interactions are rare and random collisions. The particles move in random directions, at high speeds, whose range is dependent on the temperature and defined by the Maxwell-Boltzmann distribution. Therefore, the gas phase is a completely disordered state. Following the second law of thermodynamics, gas particles will immediately diffuse to homogeneously fill any shape or volume of space that is made available to them. The thermodynamic state of a gas is characterized by its volume, its temperature, which is determined by the average velocity or kinetic energy of the molecules, and its pressure, which is determined by the average velocity and density or number of molecules. These variables are related by the fundamental gas laws, which state that the pressure in an ideal gas is proportional to its temperature and number of molecules, but inversely proportional to its volume. Like liquids and plasmas, gases are fluids: they have the ability to flow and do not tend to return to their former configuration after deformation, although they do have viscosity. Unlike liquids, however, unconstrained gases do not occupy a fixed volume, but expand to fill whatever space they occupy. The kinetic energy per molecule in a gas is the second greatest of the states of matter (after plasma). Because of this high kinetic energy, gas atoms and molecules tend to bounce off of any containing surface and off one another, the more powerfully as the kinetic energy is increased. A common misconception is that the collisions of the molecules with each other is essential to explain gas pressure, but in fact their random velocities are sufficient to define that quantity. Mutual collisions are important only for establishing the Maxwell-Boltzmann distribution. Gas particles are normally well separated, as opposed to liquid particles, which are in contact. A material particle (say a dust mote) in a gas moves in Brownian Motion. Since it is at the limit of (or beyond) current technology to observe individual gas particles (atoms or molecules), only theoretical calculations give suggestions as to how they move, but their motion is different from Brownian Motion. The reason is that Brownian Motion involves a smooth drag due to the frictional force of many gas molecules, punctuated by violent collisions of an individual (or several) gas molecule(s) with the particle. The particle (generally consisting of millions or billions of atoms) thus moves in a jagged course, yet not so jagged as we would expect to find if we could examine an individual gas molecule.

Etymology

The word "gas" was apparently coined in the early 17th century by the Belgian chemist Jan Baptist van Helmont, as a re-spelling of his pronunciation of the Greek word chaos.

Aerodynamics

Aerodynamics is a branch of fluid dynamics concerned with the study of gas flows, first analysed by George Cayley in the 1800s. The solution of an aerodynamic problem normally involves calculating for various properties of the flow, such as velocity, pressure, density, and temperature, as a function of space and time. Understanding the flow pattern makes it possible to calculate or approximate the forces and moments acting on bodies in the flow. This mathematical analysis and empirical approximation form the scientific basis for heavier-than-air flight. Aerodynamic problems can be classified 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, the shock waves that form in front of the nose of a rocket or the flow of air over a hard drive head 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. Most aerodynamicists use numbers between 5 and 8. The influence of viscosity in the flow dictates a third classification. Some problems involve only negligible viscous effects on the solution, in which case viscosity can be considered to be nonexistent. The approximations to these problems are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

Aerodynamic forces on aircraft

viscous flow One of the major goals of aerodynamics is to predict the aerodynamic forces on aircraft. The four basic forces that act on a powered aircraft are lift, weight (or gravity), thrust, and drag. Weight is the force due to gravity and thrust is the force generated by the engine. Lift and drag are forces due to the motion of the vehicle through the air. Lift is defined as the aerodynamic force acting perpendicular to the relative airflow and drag is defined as the aerodynamic force acting parallel to the relative airflow. Lift is positive upwards and drag is positive rearwards.

Aerodynamics in other fields

Aerodynamics is important in a number of applications other than aerospace engineering. It is a significant factor in any type of vehicle design, including automobiles. It is important in the prediction of forces and moments in sailing. It is used in the design of small components such as hard drive heads. Civil engineers also use aerodynamics, and particularly aeroelasticity, to calculate wind loads in the design of large buildings and bridges.

Continuity assumption

Gases are composed of molecules which collide with one another and solid objects. In aerodynamics, however, gases are considered to have continuous quantities. That is, properties such as density, pressure, temperature, 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 aerodynamics.

Conservation laws

Aerodynamic problems are solved using the conservation laws, or equations derived from the conservation laws. In aerodynamics, three conservation laws are used:
- Conservation of mass: Matter is not created or destroyed. If a certain mass of fluid enters a volume, it must either exit the volume or increase the mass inside the volume.
- Conservation of momentum: Also called Newton's second law of motion
- Conservation of energy: Although it can be converted from one form to another, the total energy in a given system remains constant. All aerodynamic problems are therefore solved by the same set of equations. However, they differ by the assumptions made in each problem. The equations become simpler as assumptions are made. Note that these laws are based on Newtonian Mechanics. They are not applicable in relativistic mechanics, which takes into account Einstein's theory of relativity. all the problem related to energy conservation must be well known

Subsonic aerodynamics

In a subsonic aerodynamic problem, all of the flow speeds are less than the speed of sound. This class of problems encompasses nearly all internal aerodynamic problems, as well as external aerodynamics for most aircraft, model aircraft, and automobiles. In solving a subsonic problem, one decision to be made by the aerodynamicist is whether or not 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 problem. When the density is allowed to vary, the problem is called a compressible problem. In air, compressibility effects can be ignored when the Mach number in the flow does not exceed 0.3. Above 0.3, the problem should be solved using compressible aerodynamics.

Transonic aerodynamics

Transonic aerodynamic problems are defined as problems in which both supersonic and subsonic flow exist. Normally the term is reserved for problems in which the characteristic Mach number is very close to one. Transonic flows are characterized by shock waves and expansion waves. A shock wave or expansion wave is a region of very large changes in the flow properties. In fact, the properties change so quickly they are nearly discontinuous across the waves. Transonic problems are arguably the most difficult to solve. Flows behave very differently at subsonic and supersonic speeds, therefore a problem involving both types is more complex than one in which the flow is either purely subsonic or purely supersonic. Š

Supersonic aerodynamics

Supersonic aerodynamic problems are those involving flow speeds greater than the speed of sound. Calculating the lift on the Concorde during cruise can be an example of a supersonic aerodynamic problem. Supersonic flow behaves very differently from subsonic flow. The speed of sound can be considered the fastest speed that "information" can travel in the flow. Gas travelling at subsonic speed diverts around a body before striking it, so it can be said to "know" that the body is there. Air cannot divert around a body when it is travelling at supersonic speeds. It subsonic flow and a diffuser in supersonic flow). Subsonic flow additional shock waves. In this case the fuselage reuses some displacement of the wings.

Hydrodynamics

Category:Fluid dynamics Hydrodynamics (literally, "water motion") is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. Blaise Pascal in the 1600s contributed some of the initial theory to this field. The term originates from the work of Daniel Bernoulli, based on the title of his work called Hydrodynamica (1738). He and Leonhard Euler established the general equations of hydrodynamics. The practice was continued by Joseph Louis Lagrange (1736-1813) with the Euler-Lagrange system, Jean le Rond d'Alembert (1717-1783) discovered the Cauchy-Riemann equations, Pierre Simon Laplace (1749-1827) with the governing equation in the potential flow named after him, Hermann Ludwig Ferdinand von Helmholtz (1821-1894) and William Thomson, Lord Kelvin (1824-1907) with Kelvin-Helmholtz instability (see also Rayleigh-Taylor and Richtmyer-Meshkov) and Helmholtz's work on vortices.

Thrust

Thrust is a reaction force described quantitatively by Newton's Second and Third Law. When a system expels or accelerates mass in one direction the accelerated mass will cause a proportional but opposite force on that system. Mathematically this means that the total force experienced by a system accelerating a mass m, is equal and opposite to the mass m times the acceleration a experienced by that mass: :F = −m·a

Examples

mass An aircraft generates forward thrust when the spinning propellers blow air, or eject expanding gases from a jet engine to the back of the aircraft. The forward thrust is proportional to the (mass of the air) multiplied by (average velocity of the airstream). Similarly, a ship generates forward thrust (or reverse thrust) when the propellers are turned to accelerate water backwards (or forwards). The resulting thrust pushes the ship in the equal and opposite direction to the sum of the momentum change in the water flowing through the propeller. A rocket (and all mass attached to it) is propelled forward by a thrust force equal to, and opposite of, the time-rate of momentum change experienced by the exhaust mass accelerating out from the combustion chamber through the rocket nozzle. This is the exhaust velocity with respect to the rocket, times the time-rate at which the mass is expelled. Of course, for a launch the thrust at lift-off should be more than the weight, and with a fair margin, because a "slow launch" would be very inefficient. Each of the three Space shuttle main engines can produce a thrust of 1.8 MN, and each of its two Solid Rocket Boosters 14.7 MN, together 34.8 MN. Compare with the mass at lift-off of 2,040,000 kg, hence a weight of 20.0 MN. The simplified Aid for EVA Rescue (SAFER) has 24 thrusters of 3.56 N each.

Parasitic drag

Parasitic drag is drag caused by moving a solid object through a fluid. Parasitic drag is made up of many components, the most prominent being form drag. Skin friction and interference drag are also major components 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. However, as speed increases the induced becomes much less, but parasitic drag necessarily increases because the fluid is flowing faster. 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 maximise endurance (minimum fuel consumption), or maximise gliding range in the event of an engine failure. Image:Drag_Curve_2.jpg Category:Fluid dynamics

Wave drag

Wave drag is an aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft flying at high-subsonic speeds.

Overview

Wave drag is caused by the formation of shock waves around the aircraft. Shock waves radiate away a considerable amount of energy, energy that is "seen" by the aircraft as drag. Although shock waves are typically associated with supersonic flow, they can form at much lower speeds at areas on the aircraft where, according Bernoulli's principle, local airflow accelerates to supersonic speeds over curved areas. The effect is typically seen at speeds of about Mach 0.8, but it is possible to notice the problem at any speed over that of the critical mach of that aircraft's wing. The magnitude of the rise in drag is impressive, typically peaking at about four times the normal subsonic drag. It is so powerful that it was thought for some time that engines would not be able to provide enough power to easily overcome the effect, which led to the concept of a "sound barrier".

Research

When the problem was being studied, wave drag came to be split into two – wave drag caused by the wing as a part of generating lift, and that caused by other portions of the plane. In 1947, studies into both problems led to the development of "perfect" shapes to reduce wave drag as much as theoretically possible. For a fuselage the resulting shape was the Sears-Haack body, which suggested a perfect cross-sectional shape for any given internal volume. The von Kármán ogive was a similar shape for bodies with a blunt end, like a missile. Both were based on long narrow shapes with pointed ends, the main difference being that the ogive was pointed on only one end.

Reduction of drag

However a number of new techniques developed during and just after World War II were able to dramatically reduce the magnitude of the problem, and by the early 1950s most fighter aircraft could reach supersonic speeds without too much trouble. If the problem of wave drag is caused by the acceleration of air over curves on the aircraft, the solution is, obviously, to reduce the curves. However this is not always easy, for instance, a wing generates lift at subsonic speeds primarily due to the curvature on the leading edge of the wing. Things are somewhat better for fuselage shaping, but simple things like a cockpit canopy or smoothing off the metal around an air intake can create additional "hot spots". These research projects were quickly put to use by aircraft designers. One common solution to the problem of wave drag due to the wings was to use a swept-wing, which had actually been developed before WWII and used on some German wartime designs (none of which saw service). Sweeping the wing to the rear makes it appear thinner and longer in the direction of the airflow, making a "normal" wing shape closer to that of the von Kármán ogive, while still remaining useful at lower speeds where curvature and thickness are important. The wing need not be swept as it is possible to build a wing that is extremely thin. This solution was used on a number of designs, perhaps the most obvious being the F-104 Starfighter. The downside to this approach is that the wing is so thin it is no longer possible to use it for fuel storage or landing gear. Fuselage shaping was similarly changed with the introduction of the Whitcomb area rule. Whitcomb had been working on testing various airframe shapes for transonic drag when, after watching a presentation by a German researcher in 1952, he realized that the Sears-Haack body had to apply to the entire aircraft. This meant that the fuselage needed to be made considerably skinnier where the wings met it, so that the cross-section of the entire aircraft matched the Sears-Haack body, not just the fuselage itself.

Other drag reduction methods

Several other attempts to reduce wave drag have been introduced over the years, but have not become common. The supercritical airfoil is a new wing design that results in reasonable low speed lift like a normal planform, but has a profile considerably closer to that of the von Kármán ogive. Although the design has been extensively tested, it has not been used, at least in a "pure" form, on any operational designs. Category:Wave mechanics Category:aerodynamics

Skin friction

In aerodynamics, skin friction is the component of parasitic drag arising from the friction of the fluid against the "skin" of the object that is moving through it. Skin friction is a function of the interaction between the fluid and the skin of the body, as well as the wetted surface, or the area of the surface of the body that would become wet if sprayed with water flowing in the wind. As with other components of parasitic drag, skin friction follows the drag equation and rises with the square of the velocity. Category:Fluid dynamics

Interference drag

In aerodynamics, interference drag is a component of parasitic drag which is caused by vortices. Whenever two surfaces meet at a sharp angle on an airplane, the airflow has a tendency to form a vortex. Accelerating the air into this vortex causes drag on the plane, and the resulting low pressure area behind the plane also contributes. Thus, the primary method of reducing interference drag is eliminating sharp angles by adding fairings which smooth out any sharp angles on the aircraft. As with other components of parasitic drag, interference drag follows the drag equation and rises with the square of the velocity. Category:Fluid dynamics

Lifting body

The lifting body is an aircraft configuration where the body itself produces lift. It is related to, but the opposite of, a flying wing, an aircraft whose fuselage is contained by the wing. In 1921 pioneering aviator and aircraft designer Vincent Justus Burnelli patented the simple concept of an airfoil shaped airframe to increase the lift and load capacity of airplanes. [http://www.aircrash.org/burnelli/chrono1.htm] Despite a number of business and political setbacks, Burnelli continued to refine and license his designs making a number of refinements to the concept up until his death in 1964. [http://www.mysteriesofcanada.com/Canada/Canada_Car/burnelli_designs.htm] [http://bennun.biz/features/burnelli.html] Aerospace related lifting body research arose from the idea of spacecraft re-entering the Earth's atmosphere and landing much like a regular aircraft. The traditional capsule-like spacecraft had very little control over where they landed once they re-entered the Earth's atmosphere. A steerable spacecraft with wings could significantly extend the landing envelope. Wings would have to be built that could withstand stresses and temperatures at hypersonic speeds. A proposed answer was to eliminate wings altogether: design the body itself to produce lift. The Space Shuttle contains some of the lifting body principles, although it relies more on the delta wing concept. NASA's refinements on the lifting body concept in 1962 with Dale Reed of NASA's Dryden Flight Research Center. The first full-size model, the NASA M2-F1, was made of wood. Initial tests were performed by towing the craft along a dry lakebed behind a modified Pontiac Catalina [http://www.classicalpontiac.com/articles/nasa.html]. Later the craft was towed from behind a C-47 and released. Since the M2-F1 was a glider, a small rocket motor was added in order to extend the landing envelope. The M2-F1 was soon nicknamed the "Flying Bathtub". In 1963, NASA began experimenting with heavier rocket powered craft dropped from a B-52 Bomber. (Of the Dryden lifting bodies, all but the NASA M2-F1 used an XLR-11 rocket engine like the famous Bell X-1.) A follow-on design was the Northrop HL-10, developed at NASA's Langley Research Center. The X-24A and X-24B were based on the M2 concept originated by Alfred Eggers in 1957 at NASA Ames Research Center (called the Ames Aeronautical Laboratory in 1957), Moffett Field, Mountain View, California. The M-2 competed in the design of the Space Shuttle. A major difficulty with these designs was air flow separation; the air stream would become very turbulent causing loss of control and lift. The HL-10 attempted to solve part of this problem by angling the port and starboard vertical stablizers outward and enlarging the center one. This air flow problem caused the crash of the Northrop M2-F2 lifting body. The rebuilt M2-F2 (now called the Northrop M2-F3) added a central rudder to correct the aerodynamic flaw of its predecessor. Much of the general public had never heard, or seen, anything about these lifting body designs until watching the 1970s television show The Six Million Dollar Man. The introduction footage showed the M2-F2, piloted by Bruce Peterson, crashing and tumbling violently along the runway. The cause of the crash was attributed to the onset of Dutch Roll. Bruce Peterson survived to fly again and, the craft was rebuilt as the M2-F3. The X-38 was a program under leadership of NASA Johnson Space Center to build a series of incremental flight demonstrators for the proposed Crew Return Vehicle (CRV) for the International Space Station. The X-38 was a lifting body based on the outer mold line of the X-24A. The lifting body concept has been considered for many other aerospace programs, including the Lockheed Martin X-33, BAC's Multi Unit Space Transport And Recovery Device, Europe's EADS Phoenix and the Russian-European cooperation Kliper spaceship. This is mainly because of the three basic shapes usually analyzed for such projects (capsule, lifting body, airplane) the lifting body offers the best trade-off on terms of maneuverability and thermodynamics. Lifting bodies, though, tend to pose complex structural and internal configuration issues.

List of Dryden Flight Research Center lifting body vehicles (1963 to 1975)

- M2-F1
- M2-F2
- M2-F3
- HL-10
- X-24A
- X-24B

Lifting body pilots and flights

- Wood, Haise and Engle each made a single, car-towed, ground flight of the M2-F1.

External links

- [http://www.dfrc.nasa.gov/Newsroom/FactSheets/FS-011-DFRC.html Lifting Bodies Fact Sheet (NASA)]
- NASA Photo Collections from Dryden Flight Research Center
- [http://www.dfrc.nasa.gov/gallery/photo/HL-10/ HL-10]
- [http://www.dfrc.nasa.gov/gallery/photo/M2-F1/ M2-F1]
- [http://www.dfrc.nasa.gov/gallery/photo/M2-F2/ M2-F2]
- [http://www.dfrc.nasa.gov/gallery/photo/M2-F3/ M2-F3]
- [http://www.dfrc.nasa.gov/gallery/photo/X-24/ X-24A and X24B]
- [http://members.lycos.co.uk/derekhorne/m2f1.html Short M2-F1 history]
- [http://www.centennialofflight.gov/essay/Evolution_of_Technology/lifting_bodies/Tech29.htm Some history of lifting body flight]
- [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980169231_1998082126.pdf Wingless Flight: The Lifting Body Story. NASA History Series SP-4220 1997 PDF] Category:Lifting bodies

Wave drag

Wave drag is an aerodynamics term that refers to a sudden and very powerful form of drag that appears on aircraft flying at high-subsonic speeds.

Overview

Research

Reduction of drag

Other drag reduction methods

Drag coefficient

The drag coefficient (C_d or C_x) is a number that describes a characteristic amount of aerodynamic drag caused by fluid flow, used in the drag equation. Two objects of the same frontal area moving at the same speed through a fluid will experience a drag force proportional to their C_d numbers. Coefficients for rough unstreamlined objects can be 1 or more, for smooth object much less. drag equation A C_d equal to 1 would be obtained in a case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. The top figure shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the left of it shows equal pressure across the surface. In a real flat plate the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges as in the lower figure and graph. The C_d of a real flat plate would be less than 1, except that there will be a negative pressure (relative to ambient) on the back surface. The overall C_d of a real square flat plate is often given as 1.17. Flow patterns and therefore C_d for some shapes can change with Reynolds number and the roughness of the surfaces.

C_d in automobiles

The drag coefficient is a common metric in automobile design, where designers strive to achieve a low coefficient. Minimizing drag is done to improve fuel efficiency at highway speeds, where aerodynamic effects represent a substantial fraction of the energy needed to keep the car moving. Indeed, aerodynamic drag increases with the square of speed. Aerodynamics are also of increasing concern to truck designers, where a lower drag coefficient translates directly into lower fuel costs. About 60% of the power required to cruise at highway speeds is taken up overcoming air drag, and this increases very quickly at high speed. Therefore, a vehicle with substantially better aerodynamics will be much more fuel efficient.

C_dA

While designers pay attention to the overall shape of the automobile, they also bear in mind that reducing the frontal area of the shape helps reduce the drag. The combination of drag coefficient and area is C_dA (or C_xA), a multiplication of the C_d value by the area, measured in m². The product of the drag coefficient and area, called drag area, was introduced in 2003 by Car and Driver as a more accurate way to compare the aerodynamic efficiency of various automobiles. Average full-size passenger cars have a drag area of roughly 8.5 ft² (.79 m²). Reported drag area ranges from the 2005 Chevrolet Corvette at 6.1 ft² (.57 m²) to the 2006 Hummer H3 at 16.8 ft² (1.56 m²).

Drag in sports and racing cars

Reducing drag is also a factor in sports car design, where fuel efficiency is less of a factor, but where low drag helps a car achieve a high top speed. However, there are other important aspects of aerodynamics that affect cars designed for high speed, including racing cars. Notably, it is important to minimize lift, hence increasing downforce, to avoid the car ever becoming airborne. Also it is important to maximize aerodynamic stability: some racing cars have tested well at particular "attack angles", yet performed catastrophically, i.e. flipping over, when hitting a bump or experiencing turbulence from other vehicles (most notably the Mercedes-Benz CLR). For best cornering and racing performance, as required in Formula 1 cars, downforce and stability are crucial and these cars have very high C_d values.

Typical values and examples

The typical modern automobile achieves a drag coefficient of between 0.30 and 0.35. SUVs, with their larger, flatter shapes, typically achieve a Cd of 0.35–0.45. Certain cars, notably can achieve figures of 0.25-0.30, although sometimes designers deliberately increase drag, in favour of reducing lift. Some notable examples:
- 2.1 - a smooth brick
- 0.9 - a typical bicycle plus cyclist
- 0.7 to 1.1 - typical values for a Formula 1 car (wing settings change for each circuit)
- at least 0.6 - a typical truck
- 0.57 - Hummer H2, 2003
- 0.51 - Citroën 2CV
- 0.42 - Lamborghini Countach, 1974
- 0.39 - Dodge Durango, 2004
- 0.38 - Volkswagen Beetle
- 0.38 - Mazda Miata, 1989
- 0.372 - Ferrari F50, 1996
- 0.36 - Citroën DS, 1955
- 0.36 - Ferrari Testarossa, 1986
- 0.36 - Citroën CX, 1974 (the car was named after the term for drag coefficient)
- 0.34 - Ford Sierra, 1982
- 0.34 - Ferrari F40, 1987
- 0.34 - Chevrolet Caprice, 1994-1996
- 0.338 - Chevrolet Camaro, 1995
- 0.33 - Dodge Charger, 2006
- 0.33 - Audi A3, 2006
- 0.33 - Subaru Impreza WRX STi, 2004
- 0.32 - Toyota Celica,1995-2005
- 0.31 - Citroën GSA, 1980
- 0.30 - Saab 92, 1947
- 0.30 - Audi 100, 1983
- 0.30 - Porsche 996, 1997
- 0.29 - Honda CRX HF 1988
- 0.29 - Subaru XT, 1985
- 0.29 - BMW 8-Series, 1989
- 0.29 - Porsche Boxster, 2005
- 0.29 - Honda Accord Hybrid, 2005
- 0.29 - Lotus Elite, 1958
- 0.28 - Toyota Camry and sister model Lexus ES, 2005
- 0.28 - Porsche 997, 2004
- 0.27 - Infiniti G35, 2002 (0.26 with "aero package")
- 0.26 - Toyota Prius, 2004
- 0.25 - Honda Insight, 1999
- 0.212 - Tatra T77, 1938
- 0.195 - General Motors EV1, 1996
- 0.19 - Mercedes-Benz "Bionic Car" Concept, 2005 (based on the boxfish)
- 0.137 - Ford Probe V prototype, 1985 Figures given are generally for the basic model. Faster and more luxurious models often have higher drag, thanks to wider tires and extra spoilers.

External links

- [http://aerodyn.org/Drag/ A. Filippone's Advanced Topics in Aerodynamics: Drag]
- [http://www.windpower.org/en/tour/wtrb/drag.htm Danish Wind Industry Association: Aerodynamics of Wind Turbines: Drag] Category:Dimensionless numbers Category:Aerospace engineering Category:Aerodynamics

Velocity

This article is about velocity in physics. For other meanings, see velocity (disambiguation). The velocity of an object is simply its speed in a particular direction. Note that both speed and direction are required to define a velocity.

Explanation

The velocity (v) is an physical quantity of the motion. A change in an object's velocity can therefore arise from either a change in its speed or in its direction. For example an aeroplane that is circling at a constant speed of 200km/h is changing its velocity because it is continously changing its direction. A aeroplane that is taking-off may go from zero to 200km/h in a straight line and so would also be changing its velocity. A change in velocity is called an acceleration. Objects are only accelerated if a force is applied to them. (The amount of acceleration depends the size of the force and the mass of the object being shifted, see Newton's Second Law of Motion.) In the case of the circling aeroplane, the pilot banks to use the force of lift from the wings to change direction. In another example the Space Shuttle orbits the earth at a constant speed but is constantly changing its velocity because of the circular orbit. In this case the force causing the acceleration is provided by the earth's gravity acting on the shuttle. The average speed v of an object moving a distance d during a time interval t is described by the formula: :

v = \frac

Acceleration is the rate of change of an object's velocity over time. The average acceleration of a of an object whose speed changes from v_i to v_f during a time interval t is given by: :

a = \frac

Where

v_i

= an object's initial velocity and

v_f

= the object's final velocity over a period of time t

Formal description

Velocity (symbol: v) is a vector measurement of the rate and direction of motion. The scalar absolute value (magnitude) of velocity is speed. Velocity can also be defined as rate of change of displacement or just as the rate of displacement, depending on how the term displacement is used. It is thus a vector quantity with dimension length/time. In the SI (metric) system it is measured in metre per second The instantaneous velocity vector v of an object that has position at time t is given by x(t) can be computed as the derivative :

v= = \lim_

The instantaneous acceleration vector a of an object that has position at time t is given by x(t) is :

\mathbf = \frac   = \frac

The equation for an object's velocity can be obtained mathematically by taking the integral of the equation for its acceleration beginning from some initial period time $t_0$ to some point in time later $t_n$ . The final velocity v_f of an object which starts with velocity v_i and then accelerates at constant acceleration a for a period of time t is: :

v_f = v_i + a t

The average velocity of an object undergoing constant acceleration is (v_i + v_f)/2. To find the displacement d of such an accelerating object during a time interval t, substitute this expression into the first formula to get: :

d = t \times \frac

When only the object's initial velocity is known, the expression :

d = v_i t + \frac

can be used. These basic equations for final velocity and displacement can be combined to form an equation that is independent of time, also known as Torricelli's Equation: :

v_f^2 = v_i^2 + 2 a d

The above equations are valid for both classical mechanics and special relativity. Where classical mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in classical mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. The kinetic energy (energy of motion) of a moving object is linear with both its mass and the square of its velocity: :

E_ = \begin \frac \end mv^2

The kinetic energy is a scalar quantity.

Polar coordinates

In polar coordinates, a two-dimensional velocity can be decomposed into a radial velocity, defined as the component of velocity away from or toward the origin, and transverse velocity, the component of velocity along a circle centred at the origin, and equal to the distance to the origin times the angular velocity. Angular momentum in scalar form is the distance to the origin times the transverse speed, or equivalently, the distance squared times the angular speed, with a plus or minus to distinguish clockwise and anti-clockwise direction. If forces are in the radial direction only, as in the case of a gravitational orbit, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as Kepler's laws of planetary motion.

Squash (sport)

Squash is an indoor racquet sport which was, until recently, called "Squash Rackets", a reference to the 'squashable' soft ball used in the game (compared with the harder ball used in its parent game Racquets or Rackets--see below). The game is played by two players, with 'standard' rackets (or occasionally four players for doubles) in a four-walled court with a small, hollow rubber ball.

History

Squash historians assert that the game originated in the 19th century at the Harrow School, just outside London in England, as a derivative of the game of Racquets. The first recorded construction of purpose-built squash courts was at Harrow in the 1860s. It is possible that earlier squash courts were created at Harrow by sub-dividing a racquets court, which is almost exactly the size of three Squash courts (to allow more players on the courts at the same time). The game generally remained the preserve of the schools and universities until the early part of the 20th century, by which time it was becoming popular in the private clubs (such as the RAC in London) and with officers in the British armed forces. The U.S.A. became the first nation to form a dedicated association and codify its game in 1907. In the same year, the (English) Tennis and Rackets Association formed a squash rackets sub-committee to administer the game, which became progressively codified during the 1920s. Subsequently, the (English) Squash Rackets Association was formed and took over administration of the game in 1928. The game is now administered by the WSF (World Squash Federation). The men's professional game is managed by the PSA (Professional Squash Association) and the women's by WISPA (Women's International Squash Players Association). Squash continued almost exclusively as the game of the upper-middle and/or upper class(es) until around the 1950's, when commercial operators began building public courts. The game boomed in popularity, with participation peaking around the early 1980's. Despite a downturn in player numbers, the game remains popular in many places, especially Australia, northwestern Europe, North America and Asia (primarily the south and southeastern regions thereof). At the elite level, the game was strictly divided between amateur players (usually 'gentlemen' and 'ladies') and professional players, who were often coaches employed by the exclusive clubs. This division started to break down with the growth of the commercial side of the game in the 1960s, with the women's game becoming 'open' in 1973 and the men's game in 1980.

The playing area

Courts are usually constructed with masonry walls, finished with a smooth render and painted white with red 'out' and 'service' lines. Many modern courts have been constructed with a see-through glass backwall, and professional matches are sometimes played on an 'all-glass' court, allowing viewing by up to 2000 spectators. Recently, some clubs have constructed 'rainbow courts' with green or blue walls, much to the disapproval of traditionalists. The floor is usually a light-coloured timber strip flooring laid longitudinally and sprung, with red line markings for the service boxes and service areas. The ceiling should be light-coloured and high enough to permit the ball to be 'lobbed' (hit in a high arc to the back of the court). In the more popular and widespread 'International' (originally English) version of the game, the court is 9.75 m (32 feet) long by 6.4 m (21 feet) wide. The 'American' version of the game uses a harder ball and a court 18 feet (5.49 m) wide. There is a hollow metal panel along the base of the front wall called the 'tin', analogous to the net in tennis (it is designed this way to make a loud noise when the ball strikes it). It is surmounted by a 50 mm (2 inches) high 'board', on international courts reaching a total height of 480 mm (19 inches). 'Out' lines, 2.13 m (7 feet) high at the back wall and 4.57 m (15 feet) at the front wall, are joined by a raking 'out' line on each side wall. On American-style courts the tin is two inches lower, thus 17 inches high. On an American court the sidewall 'out' lines also stay horizontal from the front wall all the way to the back.

Playing equipment

'Standard' rackets are governed by the rules of the game. Traditionally they were made of laminated timber, with a small strung area using natural 'gut' strings. After a rule change in the mid-1980's, they are now almost always made of ceramic materials (graphite, kevlar, titanium, and/or boron) with synthetic strings. Modern rackets are 70 cm (27 inches) long, with a maximum strung area of 500 square centimetres (approximately 80 square inches) and a weight between 110 and 200 grams (4-7 ounces). The balls (manufactured by Dunlop, Prince, Pointfore and others) are made from two pieces of highly durable rubber compound glued together and buffed to a matte finish. Different balls are provided for the varying conditions and standards of play: less experienced players are able to use balls that are bouncier and larger than those used by more experienced players. Small coloured dots on the ball indicate the level of bounciness and hence, the standard of play it is suited for. A bouncier ball is said to be "fast" whereas a less bouncy ball is said to be "slow". The ball becomes more bouncy as the temperature of the ball increases. Pro players generally hit much harder and have longer rallies, and therefore play with a ball at a much hotter temperature than amateurs. The "faster" balls actually allow amateurs to play the game with the SAME amount of ball bounce as the pros, a fact that many club-level players are not aware of. Many club players end up playing "dead ball" squash because they use a ball which isn't suited for their level of play. [http://www.ithacasquash.com/ball/ball.html] The recognised colours are:
- Double Yellow - Extra Super Slow
- Yellow - Super Slow
- Green or White - Slow
- Red - Medium
- Blue - Fast The 'double-yellow dot ball', introduced in 2000, is currently the competition standard. Prior to this the yellow-dot was long considered standard. There is also a high-altitude ball, used in places like Mexico City and Denver. Because of the vigorous nature of the game, players need to wear comfortable sports clothing and robust indoor (non-marking) sports shoes. Towelling wrist and head bands may also be required in humid climates. Eye protection with polycarbonate lenses is also recommended, as players may be struck by a fast-swinging racket or the ball, which can typically reach speeds of up to 200 km/h (125 mph) - in the 2004 Canary Wharf Squash Classic, John White was recorded driving balls at speeds over 270 km/h (170 mph). Many squash venues require the use of eye protection.

The play and scoring

The players take turns hitting the ball against the front wall (referred to as 'rallying'). The ball may be volleyed (hit on the full) or hit after its first bounce. To be considered 'good', the ball must reach the front wall below the 'out' line and above the 'board' or 'tin', before touching the floor. The ball may also be struck against any of the other three walls before and/or after reaching the front wall. Shots that are first played off the side or back walls are referred to as 'boasts' or 'angles'. The rally continues until a player is unable to return his or her opponent's shot or makes a mistake (e.g. hits the ball 'out', or hits it after its second bounce, or onto the floor, 'board' or 'tin'), or a 'let' or 'stroke' is awarded by the referee for interference (see below). In the 'traditional' English scoring system (as adopted in 1926), a point is scored only by the server (when the receiver is unable to return the ball to the front wall before it has bounced twice). When the receiver wins the rally, they are awarded only the right to serve. Games are usually played to 9 points (alternatively, the receiver may opt to call 'set two' and play to 10 when the score first reaches 8-8). Competition matches are usually played to 'best-of-five' (ie. first player to win 3 games wins the match). Alternatively, in the point-a-rally scoring system (referred to as PARS or 'American' scoring), points are scored by the winner of each rally, whether or not they have served. Traditionally, PARS scoring was up to 15 points (or the receiver calls 15 or 17 when the game reaches 14 all). However, in 2004, the PARS scoring was reduced to 11 for the professional game (If the game reaches 10 all, a player must win with two consecutive points with the serve). In the 'international' game, club, doubles and recreational matches are usually played using the traditional 'English' scoring system.

Strategy and tactics

The fundamental strategy of the game is to hit the ball straight up the side walls to the back corners (referred to as a 'good length' shot or 'rail'), then move to the centre of the court to be well placed to retrieve the opponent's return. Attacking with soft shots to the front corners (referred to as 'drop shots') causes the opponent to cover more of the court and may result in an outright winner. 'Angle' shots (see above) are used for deception and again to cause the opponent to cover more of the court. Highly-skilled players often attempt to finish rallies by hitting the ball at an angle onto the front wall and into an area known as the 'nick' (the junction between the side wall and floor) which if done properly will cause the ball to roll out along the floor and be unreturnable. If the shot misses the nick, however, the ball may bounce out from the side wall and allow the opponent an easy attacking shot. Perhaps the one key strategy in squash is known as "dominating the T". The T is the place near the centre of the court which gives the player the most options for moving towards the ball. Really skilled players will return a shot, and then move back toward the T before playing the next. From this position, the player can access any part of the court within two steps.

Interference and obstruction

Interference and obstruction are an inevitable aspect of this highly athletic sport, where two players are confined within a shared space. Generally, the rules entitle players to reasonable access to the ball, a reasonable swing and an unobstructed shot to any part of the front wall. When interference occurs, a player may appeal for a 'let' and the referee (or the players themselves if there is no official) then interprets the extent of the interference. The referee may elect to allow a 'let' and the players then replay the point, or award a 'stroke' (either a point or the right to serve) to the appealing player, depending on the degree of interference. When it is deemed that there has been little or no interference, the rules decree that no let is to be allowed, in the interests of continuity of play and the discouraging of spurious appeals for lets. Because of the subjectivity in interpreting the nature and magnitude of interference, the awarding (or withholding) of lets and strokes is often controversial.

Cultural and social aspects of squash

The relatively small court and low-bouncing ball makes the game harder to master than its American cousin racquetball, as the ball may be played to all four corners of the court. Since every ball must strike the front wall above the tin (unlike racquetball), the ball cannot be easily killed. As a result, rallies tend to be longer than in racquetball. Also, the better one gets in racketball the shorter the rallys, in squash the better one gets the longer the rallys. Squash provides an excellent cardio-vascular workout. In one hour of squash, a player may expend 700 to 1000 calories (3,000 to 4,000 kJ) which is significantly more than most other sports. The sport also provides a good upper and lower body workout by utilising both the legs to run around the court and the arms/torso to swing the racquet. There are several variations of squash played across the world. In the US 'hardball' singles and doubles are played with a much harder ball and different size courts (as noted above). Whilst 'hardball' singles has lost much of its popularity in North America (in favor of the 'International' version), the hardball doubles game is still active. There is also a doubles version of squash played with the standard ball, sometimes on a wider court, and a more tennis-like variation known as squash tennis. Squash games are most competitive and enjoyable when played between players of similar skill levels. However there is no international standard method for evaluating the players' skill levels. This creates a rather interesting phenomenon within the squash community: many squash players are constantly on the look-out for potential partners who are compatible physically, mentally, and technically. Squash now has a universal appeal, as there are courts in 148 countries in the world from Argentina to Zambia.

Players and records

The (English) Squash Rackets Association conducted its first British Open championship for men in 1930, using a 'challenge' system: Charles Read was designated champion, but was beaten in home and away matches by Don Butcher. This championship continues to this day, but now using a knockout format since 1947. Since its inception, the men's British Open has been dominated by relatively few players: F. D. Amr Bey (Egypt) in the 1930s; Mahmoud Karim (Egypt) 1940s; brothers Hashim and Azam Khan (Pakistan) 1950s and 1960s; Jonah Barrington (Great Britain and Ireland) and Geoff Hunt (Australia) 1960s and 1970s; Jahangir Khan (Pakistan) 1980s; Jansher Khan (Pakistan) 1990s. Recent championships have been shared by players from England, Scotland, Wales, Australia and Canada. The women's championship started in 1921, and has similarly been dominated by relatively few players: Nancy and Joyce Cave (England) in the 1920s; Margot Lumb (England) 1930s; Janet Morgan (England) 1950s; Heather McKay (Australia) 1960s and 1970s; Susan Devoy (New Zealand) 1980s; Michelle Martin (Australia) 1990s. The current defending champion is Nicol David of Malaysia. Because of its traditions, the British Open is considered by many to be more prestigious than the world championships, which began in the mid-1970s. Heather McKay, with her lengthy and absolute dominance of the game during the 1960s and 1970s, is undoubtedly the greatest woman player of all time. Amongst the men, most modern commentators consider Hashim Khan (1950s) or (the unrelated) Jahangir Khan (1980s) to be the greatest male players. Other worthy contenders are Jonah Barrington, Geoff Hunt and Jansher Khan.

References

-
-

External links

- [http://www.geocities.com/colosseum/court/4161/ Cyrus' Squash Coaching Site]
- [http://www.ispsquash.com Indian Squash Professionals]
- [http://www.squashplayer.co.uk Squashplayer magazine]
- [http://www.nwcsl.resultszone.com North West Counties Squash League UK, largest squash league in the world]
- [http://indiansquash.net/ Squash Raquets Federation of India]
- [http://www.squashmagazine.com Squash Magazine, monthly magazine includes news, profiles, training information]
- [http://www.squashtalk.com SquashTalk, has squash hall of fame, historical information, current news]
- [http://www.geocities.com/nicolanndavidsquash Nicol David (2005 women's squash world champion)]
- [http://www.collegesquash.org College Squash Association, has complete details on intercollegiate squash in the USA]
- [http://worldsquash.org World Squash Federation, has more details on rules, rankings and court dimensions]
- [http://squashclub.org SquashClub.org, an online community of squash players]
- [http://www.ncsra-squashwars.org/ Washington DC squash links]
- [http://www.ropeyladder.com/squash/ RopeyLadder.com, an online system for running competitive squash ladders]
- [http://www.squashtalk.com/profiles/fameprofiles.htm Squash Hall of fame]
- [http://www.englandsquash.com/ England Squash]
- [http://www.squashgame.info/ SquashGame.info, Squash resources and discussion] Category:Ball games
- ko:스쿼시 (운동) ja:スカッシュ (スポーツ) nb:Squash (sport)

Drag Resistant Aerospike

A Drag Resistant Aerospike is a telescoping outward extension that reduces frontal drag on missiles. In 1995 at the 33rd Aerospace Sciences Meeting it was reported that tests were performed at an aerospike-protected missile dome to Mach 6 to obtain quantitative surface pressure and temperature-rise data on the Feasibility of an aerospike for hypersonic missiles. This not only has a use in space travel but also weapons grade missiles. The Trident missile system uses this to reduce its drag by up to 50 percent. The aerospike serves to form a sort of pilot hole which initiates a shockwave or channel in the airstream and reduces the amount of resistance on the main missile body. Similar systems are also seen on supersonic aircraft.

External links

- http://techreports.larc.nasa.gov/ltrs/PDF/aiaa-95-0737.pdf. Category:Aerodynamics

Added mass

Added mass is the weight added to a system due to the fact that an accelerating or decelerating body must move some volume of surrounding fluid with it as it moves. The added mass force opposes the motion, and acts as a kind of drag force. Not to be confused with relativistic mass increase.

Applications

The added mass can be incorporated into most physics equations by considering an effective mass as the sum of the mass and added mass. That is, F = m
- a becomes F = (m + added mass)
- a. Added mass for a sphere = :

\frac

r = radius of the sphere Added mass for a cylinder = Density of liquid
- Volume of Cylinder

References

[http://web.mit.edu/2.016/www/labs/L01_Added_Mass_050915.pdf MIT OpenCourse Ware] Category:Fluid dynamics

Category:Force

Category:Nature Category:Fundamental physics concepts Category:Physical quantity

Category:Theodore Roosevelt

Category:Roosevelt Roosevelt, Theodore

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Drag (physics)

See also

Drag (disambiguation)

Fluid

See also

Gas

Properties of a gas

Etymology

See also

Aerodynamics

Aerodynamic forces on aircraft

Aerodynamics in other fields

Continuity assumption

Conservation laws

Subsonic aerodynamics

Transonic aerodynamics

Supersonic aerodynamics

See also

Hydrodynamics

See also

Thrust

Examples

See also

Parasitic drag

Wave drag

Overview

Research

Reduction of drag

Other drag reduction methods

Skin friction

Interference drag

Lifting body

List of Dryden Flight Research Center lifting body vehicles (1963 to 1975)

Lifting body pilots and flights

External links

Wave drag

Overview

Research

Reduction of drag

Other drag reduction methods

Drag coefficient

Cd in automobiles

CdA

Drag in sports and racing cars

Typical values and examples

See also

External links

Velocity

Explanation

Formal description

Polar coordinates

See also

Squash (sport)

History

The playing area

Playing equipment

The play and scoring

Strategy and tactics

Interference and obstruction

Cultural and social aspects of squash

Players and records

See also

References

External links

Drag Resistant Aerospike

See also

External links

Added mass

Applications

References

Category:Force

Category:Theodore Roosevelt

Áreas del conocimiento

Campos de Read More...

Información General

Límites

Historia

Geografía

Origen del término

Biografía

C_d in automobiles

C_dA

Campos de

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