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Drag

Drag

: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

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.

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.

Force

:For other senses of this word, see force (disambiguation). In physics, a force is an external cause responsible for any change of a physical system. For instance, a person holding a dog by a rope is experiencing the force applied by the rope on their hand, and the cause for its pulling forward is the force exercised by the rope. The kinetic expression of this change is, according to Newton's second law, acceleration, non kinetic expressions such as deformation can also occur. The SI unit for force is the newton.

Elementary concepts

Force in its most primitive definition can be thought of as that which when acting alone causes an object to accelerate. In a practical sense forces can be divided into two groups: contact forces and field forces. Contact forces require the physical contact of one object with other such as a hammer striking a nail or the force exerted by a gas under pressure - gas produced by exploding gunpowder forces a heavy ball out of a cannon. Field forces on the other hand need no physical medium of contact. Gravity and magnetism are examples of such forces. It should be noted however, that fundamentally all forces are in fact field forces. The force of hammer striking the nail in the previous example turns out to be a clash of the electric forces in both hammer and nail. Nevertheless it is appropriate in some cases to maintain these two classifications for ease of understanding.

Quantitative definition

In physics models, the point-like system is used, where objects are represented as one-dimensional points at their centre of mass. The only change the system can experience is a change of its momentum (its speed). Since the rise of the atomic theory, any physical system has been considered in classical physics as composed of point-like systems called atoms or molecules. Therefore, all forces can be defined by their effect; that is, by the change of movement they induce on point-like systems. This change of movement can be quantified by the acceleration (the derivative of velocity). The discovery by Isaac Newton that a given force will induce an acceleration in inverse proportion to a quantity called the mass of inertia or inertial mass which is independent of the speed of the system is Newton's second law. This law allows us to predict the effect of a force on any point-like system whose mass is known. It is usually written as: :F = dp/dt = d(m·v)/dt = m·a (in the case where m does not depend on t) where :F is the force (a vector quantity), :p is the momentum, :t is the time, :v is the velocity, :m is the mass, and :a=d²x/dt² is the acceleration, the second derivative with respect to t of the position vector x. If the mass m is measured in kilograms and the acceleration a is measured in metres per second squared, then the unit of force is kilogram × metre/second squared. This unit is called the newton: 1 N = 1 kg x 1 m/s². This equation is a system of three second-order differential equations with respect to the three-dimensional position vector which is an unknown function of time. This equation can be solved if F is a known function of x and some of its derivatives and if the mass m is known. Morevover the boundary conditions are required; for example, the values of the position vector and x and the velocity v at the starting time, say t=0. Of course, this formula is only useful if one knows the numerical values of F and m. The definition above is an implicit definition, arrived at as follows. One defines a reference system (one litre of water) and a reference force (the gravitational force applied by the Earth on it at the altitude of Paris). One takes Newton's second law for granted (one postulates that it is true) and measures the acceleration induced by the reference force on the reference system. This gives us a mass unit (1 kg) and a force unit (the older unit of 1 kilogram-force = 9.81 N). Once this is done, one can measure any force by the acceleration it induces on the reference system and measure the inertial mass of any system by measuring the acceleration induced on this system by the reference force. Force is often considered a fundamental quantity in physics, but there are more fundamental quantities, such as momentum (p = mass m x velocity v). Energy, measured in joules, is still less fundamental than force and momentum, because it is defined as work, and work is defined in terms of force. The two most fundamental theories of nature - quantum electrodynamics and general relativity - do not contain the concept of force at all. Although not the most fundamental quantity in physics, force is an important basic mathematical concept from which other concepts, such work and pressure (measured in pascals), are derived. Force is sometimes confused with stress.

Types of force

There are four known fundamental forces in nature.
- Nuclear forces acting between subatomic particles
- Electromagnetic forces between electric charges
- Weak forces arising from radioactive decay
- Gravitational forces between masses Quantum field theory accurately models the first three fundamental forces, but does not model quantum gravity. Quantum gravity on a large scale can, however, be described by general relativity. The four fundamental forces describe every observable phenomenon including the many other forces observed such as: Coulomb's force (the force between electrical charges), gravitational force (force between masses), magnetic force, frictional forces, centripetal, centrifugal, impact force, and spring force, to name a few. Forces can also be classified into conservative forces and nonconservative forces. Conservative forces are equivalent to the gradient of a potential, and include gravity, electromagnetic force, and spring force. Nonconservative forces include friction and drag.

Properties of force

Because momentum is a vector, then force, being its time derivative, is also a vector - it has magnitude and direction. Forces can be added together using the parallelogram of force. When two forces act on an object, the resulting force, the resultant, is the vector sum of the original forces. This is called the principle of superposition. The magnitude of the resultant varies from zero to the sum of the magnitudes of the two forces, depending on the angle between their lines of action. If the two forces are equal, but opposite, the resultant is zero. This condition is called static equilibrium, with the result that the object remains at rest or moves with a constant velocity. As well as being added, forces can be can also be broken down (or 'resolved'). For example, a horizontal force pointing northeast can be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Force vectors can also be three-dimensional, with the third (vertical) component at right-angles to the two horizontal components.

Forces in theory

The total (Newtonian) force, in newtons, on an object at any given time is defined as the rate of change of the object's velocity multiplied by the object's mass: :

\mathbf = \lim_ \frac

where :m is the inertial mass of the particle (measured in kilograms) :v_o is its initial velocity (measured in metres per second) :v is its final velocity (measured in metres per second) :T is the time from the initial state to the final state (measured in seconds); :Lim T→0 is the limit as T tends towards zero. Force was so defined to explain the effects of superimposing situations: if in one situation, a force is experienced by a particle, and if in another situation another force is experienced by that particle, then in a third situation, which (according to standard physical practice) is taken to be a combination of the two individual situations, the force experienced by the particle will be the vector sum of the individual forces experienced in the first two situations. This superposition of forces, and the definition of inertial frames and inertial mass, are the empirical content of Newton's laws of motion. There are other ways to look at the above definition of force. First, the mass of a body multiplied by its velocity is called its momentum, p, so the above definition is equivalent to: :

\textbf=

If F is not constant over Δt, then this is the definition of average force over the time interval. To apply it at an instant we apply an idea from calculus. If we graph p as a function of time, the average force will be the slope of the line connecting the momentum at two times. Taking the limit as the two times get closer together gives the slope at an instant, which is called the derivative: :

\textbf=

Many forces are associated with a potential energy field. For instance, the gravitational force acting upon a body can be seen as the action of the gravitational field that is present at the body's location. The potential field is defined as that field whose gradient is equal and opposite to the force produced at every point: :

\textbf=-\nabla U

The derivative of force with respect to time is called yank. Higher order derivatives are sometimes used, but they lack names because of their rarity. In most explanations of mechanics, force is usually defined only implicitly, in terms of the equations that work with it. Some physicists, philosophers and mathematicians, such as Ernst Mach, Clifford Truesdell and Walter Noll, have found this problematic and sought a more explicit definition of force. According to the Special theory of relativity the mass of an object increases as it's velocity and therefore it's energy increases. The law of force must then be modified to the following: :

\textbf=

where :v is the mass's velocity :c is the speed of light. Note that the equation is undefined if the mass's speed is equal to c because one then has to divide by zero. This is one reason most physicists believe an object with nonzero rest mass can not be accelerated to the speed of light, as this would require an infinite force.

Units of measurement

The SI unit used to measure force is the newton (symbol N), which is equivalent to kg·m·s⁻².

Non-SI units of force and mass

The F=m·a relationship can be used with any consistent units (SI or CGS). If these units are not consistent, a more general form, F=k·m·a, can be used, where the constant k is a conversion factor dependent upon the units being used. For example, in imperial engineering units, F is measured in "pounds force" or "lbf", m in "pounds mass" or "lb", and a in feet per second squared. In this particular system, one needs to use the more general form above, usually written F=m·a/g_c with the constant normally used for this purpose g_c = 32.174 lb·ft/(lbf·s²) equal to the reciprocal of the k above. As with the kilogram, the pound is colloquially used as both a unit of mass and a unit of force. 1 lbf is the force required to accelerate 1 lb at 32.174 ft per second squared, since 32.174 ft per second squared is the standard acceleration due to terrestrial gravity. Another imperial unit of mass is the slug, defined as 32.174 lb. It is the mass that accelerates by one foot per second squared when a force of one lbf is exerted on it. When the standard gee (an acceleration of 9.80665 m/s²) is used to define pounds force, the mass in pounds is numerically equal to the weight in pounds force. However, even at sea level on Earth, the actual acceleration of free fall is quite variable, over 0.53% more at the poles than at the equator. Thus, a mass of 1.0000 lb at sea level at the equator exerts a force due to gravity of 0.9973 lbf, whereas a mass of 1.000 lb at sea level at the poles exerts a force due to gravity of 1.0026 lbf. The normal average sea level acceleration on Earth (World Gravity Formula 1980) is 9.79764 m/s², so on average at sea level on Earth, 1.0000 lb will exerts a force of 0.9991 lbf. The equivalence 1 lb = 0.453 592 37 kg is always true, by definition, anywhere in the universe. If you use the standard gee which is official for defining kilograms force to define pounds force as well, then the same relationship will hold between pounds-force and kilograms-force (an old non-SI unit is still used). If a different value is used to define pounds force, then the relationship to kilograms force will be slightly different—but in any case, that relationship is also a constant anywhere in the universe. What is not constant throughout the universe is the amount of force in terms of pounds-force (or any other force units) which 1 lb will exert due to gravity. By analogy with the slug, there is a rarely used unit of mass called the "metric slug". This is the mass that accelerates at one metre per second squared when pushed by a force of one kgf. An item with a mass of 10 kg has a mass of 1.01972661 metric slugs (= 10 kg divided by 9.80665 kg per metric slug). This unit is also known by various other names such as the hyl, TME (from a German acronym), and mug (from metric slug). Another unit of force called the poundal (pdl) is defined as the force that accelerates 1 lbm at 1 foot per second squared. Given that 1 lbf = 32.174 lb times one foot per second squared, we have 1 lbf = 32.174 pdl. The kilogram-force is a unit of force that was used in various fields of science and technology. In 1901, the CGPM improved the definition of the kilogram-force, adopting a standard acceleration of gravity for the purpose, and making the kilogram-force equal to the force exerted by a mass of 1 kg when accelerated by 9.80665 m/s². The kilogram-force is not a part of the modern SI system, but is still used in applications such as:
- Thrust of jet and rocket engines
- Spoke tension of bicycles
- Draw weight of bows
- Torque wrenches in units such as "meter kilograms" or "kilogram centimetres" (the kilograms are rarely identified as units of force)
- Engine torque output (kgf·m expressed in various word orders, spellings, and symbols)
- Pressure gauges in "kg/cm²" or "kgf/cm²" In colloquial, non-scientific usage, the "kilograms" used for "weight" are almost always the proper SI units for this purpose. They are units of mass, not units of force. The symbol "kgm" for kilograms is also sometimes encountered. This might occasionally be an attempt to disintinguish kilograms as units of mass from the "kgf" symbol for the units of force. It might also be used as a symbol for those obsolete torque units (kilogram-force metres) mentioned above, used without properly separating the units for kilogram and metre with either a space or a centered dot.

Conversions

Below are several coversion factors between various mesurements of force:
- 1 kgf (kilopond kp) = 9.80665 newtons
- 1 metric slug = 9.80665 kg
- 1 lbf = 32.174 poundals
- 1 slug = 32.174 lb
- 1 kgf = 2.2046 lbf

Forces in everyday life

Forces are part of everyday life, with examples such as:
- gravity: objects fall, even after being thrown upwards, or slide and roll down
- friction: floors and objects that are not extremely slippery
- spring force, objects resist tensile stress, compressive stress and/or shear stress, objects bounce back.
- electromagnetic force: attraction of magnets
- movement created by force: the movement of objects when force is applied.

Forces in the laboratory

Founding experiments

- Galileo Galilei used rolling balls to disprove the Aristotelian theory of motion (1602 - 1607)
- Henry Cavendish's torsion bar experiment measured the force of gravity between two masses (1798)

Instruments to measure forces

- spring balance
- pivot balance
- forcemeter

History

Force was first described by Archimedes.

References

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External links

- [http://jumk.de/calc/force.shtml Calculation: force F - English and American units to metric units]
- [http://calc.skyrocket.de/en/ Online Unit Converter - Conversion of many different units]
- [http://www.patbelford.com/gallery/web3d/education/forceworkpower/index.html Interactive demonstration of Force-Work-Power Relationship] Category:Introductory physics ko:힘 ms:Daya (fizik) ja:力 simple:Force (physics)

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.

Lift-induced drag

In aerodynamics, lift-induced drag, or more simply, induced drag, is a drag force arising from the generation of lift by wings or a lifting body during flight. Induced drag will be present whenever the wings are producing lift. To that extent, it is often said that induced drag is a part of lift. It arises from the downwash induced by the wingtip and trailing edge vortices which, for a given amount of lift being produced, tilts the total reaction force further backwards through the induced downwash angle. This extra rearward tilt, in effect, increases the length of the drag vector and it is this increase in drag which is known as induced drag. The angle through which the Total Reaction tilts towards the rear is determined by the pressure distribution and the direction of the effective airflow. By definition, the lift and drag components of the Total Reaction must be resolved with respect to the remote relative airflow which reflects the direction of flight. Obviously, the smaller the angle of induced downwash, the lower will be the induced drag. There are a number of factors affecting induced drag:

Aspect Ratio

High aspect ratio wings produce smaller vortices and, in comparison with a wing of lower aspect ratio, proportionally less of the airflow swept by the longer span is affected by the vortices. Consequently, the induced downwash angle when averaged over the whole of the high aspect ratio wing, is smaller and the induced drag is low. To minimise lift-induced drag, gliders have very high aspect ratios. Induced drag is directly related to the speed of an aircraft. This means that as an airplne increases it's velocity the amount of induced drag will increase.

Wing Planform

For a wing of given span, an elliptical planform produces the smallest vortices and therefore the lowest induced drag. Because of their difficulty in construction not many aircraft have been built with this planform — perhaps the most famous example being the World War II Spitfire. However, for wings with straight leading and trailing edges, the judicious use of taper and washout of the wing sections toward the tips can produce a similar reduction in induced drag. Most straight wings produce between 5–15% more induced drag than an elliptical wing and this is accounted for by the wing efficiency factor.

Coefficient of Lift

From the pilot's point of view, where the aspect ratio and planform of the aircraft are fixed, the important factors in determining induced drag are angle of attack, airspeed and aircraft weight. These are incorporated in the induced drag formula which can be seen to have a powerful effect on the amount of induced drag generated. :Angle of attack :Induced drag increases as the angle of attack is increased. The strength of the vortices is determined by the pressure difference above and below the wing. When the wing is at the zero-lift angle of attack (AoA -2° / CL = 0) there are no vortices and therefore no induced drag. As the angle of attack is increased, vortices form and increase in strength up to the angle of attack for CL Max, typically 16° (varies between aircraft). Induced drag therefore increases with angle of attack to be at a maximum at the stalling angle. :Airspeed :Induced drag is inversely proportional to the square of the indicated airspeed (IAS). This is the opposite to the effect of airspeed on parasite drag, which is directly proportional to IAS². When the factors of angle of attack and airspeed are combined, induced drag is greatest at low airspeeds and at high angles of attack. For an aircraft just after takeoff for example, induced drag can be as high as 75% of total drag. When an aircraft is manoeuvering at high speed, although induced drag is proportionally lower, it is still significant because of the high angle of attack being used. :Weight :Increased weight means that higher angles of attack must be used to produce a given amount of lift for a given speed. Induced drag increases in proportion to weight squared (W²). An alternative way of looking at induced drag is as follows. The production of vortices is an inevitable consequence of the production of lift with a wing of finite span. These vortices result in an induced downwash which is over and above the downwash necessary to produce lift. To produce a rotary motion of any fluid requires energy — an example is the energy requred to stir a large volume of water in a drum with some sort of paddle. In flight, the energy required to create the vortices must be sourced from somewhere. Ultimately, that demand is placed on the engine by requiring higher power to be used to offset the induced drag when it is desired to maintain a given speed. A hypothetical wing of infinite span (no wing tips) would not produce vortices; would have "zero" induced angle of attack and would therefore produce no induced drag. Given the impracticality of building a tip-less wing, aircraft manufacturers have instead designed small fins at the wing tips called winglets to minimise the vortices. Wingtip tanks have a similar effect. Induced drag must be added to the parasitic drag to find the total drag. As discussed above, induced drag becomes less of a factor the faster the aircraft flies because at higher speeds a smaller angle of attack is required for the same amount of lift. The opposite occurs with parasitic drag (the drag caused simply by pushing the aircraft through the air), which increases with 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 use this speed when it is necessary to maximise endurance (minimum fuel consumption and maximum time aloft), or maximise gliding range in the event of an engine failure or when engaged in the sport of gliding. In practice, this airspeed corresponds to that resulting from the minimum power required to maintain level flight.

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

Wing

:For some other uses of the word "wing" please see Wing (disambiguation). Wing (disambiguation).]] Wing (disambiguation) A wing is a surface used to produce an aerodynamic force normal to the direction of motion by travelling in air or another gaseous medium, facilitating flight. It is a specific form of airfoil. The first use of the word was for the foremost limbs of birds, but has been extended to include other animal limbs and man-made devices. A wing is an extremely efficient device for generating lift. Its aerodynamic quality, expressed as a Lift-to-drag ratio, can be up to 60 on some gliders and even more. This means that a significantly smaller thrust force can be applied to propel the wing through the air in order to obtain a specified lift.

Use

The most common use of wings is to fly by deflecting air downwards to produce lift, but upside-down wings are also commonly used as a way to produce downforce and hold objects to the ground (for example racing cars). A sailing boat moves by using its sails as wings to produce lift (in the horizontal plane) from the force of the wind.

Artificial wings

Terms used to describe aeroplane wings

Image:Aircraft wing flaps small dsc06830.jpg|Flaps partially deployed Image:Aircraft wing flaps full dsc06835.jpg|Full flaps Image:Aircraft wing flaps full airbrakes dsc06838.jpg|Full flaps, with airbrakes and spoilers deployed for ground braking
- Leading edge: the front edge of the wing
- Trailing edge: the back edge of the wing
- Span: distance from wing tip to wing tip
- Chord: distance from wing leading edge to wing trailing edge, usually measured parallel to the long axis of the fuselage
- Aspect ratio: ratio of span to standard mean chord
- Aerofoil (or Airfoil in US English): the shape of the top and bottom surfaces when viewed as cross sections cut from leading edge to trailing edge.
- Sweep angle: the angle between the perpendicular to the design centreline of the wing in the wing plane, and either the leading edge or 1/4 chord line.
- Twist: gradual change of the airfoil (aerodynamic twist) and/or angle of incidence of the wing cross-sections (geometrical twist) along the span.

Design features

Aeroplane wings may feature some of the following:
- A rounded (rarely sharp) leading edge cross-section
- A sharp trailing edge cross-section
- Leading-edge devices such as slats, slots, or extensions
- Trailing-edge devices such as flaps
- Ailerons (usually near the wingtips) to provide roll control
- Spoilers on the upper surface to disrupt lift and additional roll control
- Vortex generators to help prevent flow separation
- Wing fences to keep flow attached to the wing
- Dihedral, or a positive wing angle to the horizontal. This gives inherent stability in roll. Anhedral, or a negative wing angle to the horizontal, has a destabilising effect
- Folding wings allow more aircarft to be carried in the confined space of the hangar of an aircraft carrier.

Wing types

- Swept wings are wings that are bent back at some angle, instead of sticking straight out from the fuselage.
- Forward-swept wings are high performance wings that are bent forward, the reverse of a traditional swept wing. Forward swept wings are also used in some two seat gliders.
- Elliptical wings (technically wings with an elliptical lift distribution) are theoretically optimum for efficiency at subsonic speeds.
- Delta wings have reasonable performance at subsonic and supersonic speeds and are good at high angles of attack.
- Waveriders are efficient supersonic wings that take advantage of shock waves.
- Rogallo wings are two hollow half-cones of fabric, one of the simplest wings to construct.
- Swing-wings (or variable geometry wings) are able to move in flight to give the benefits of dihedral and delta wing. Although they were originally proposed by German aerodynamicists during the 1940s, they are currently only found on some military aircraft such as the Grumman F-14, Panavia Tornado, General Dynamics F-111, B-1 Lancer, Tupolev Tu-160, MiG-23 and Sukhoi Su-24.
- Ring wings are optimally loaded closed lifting surfaces with higher aerodynamic efficiency than planar wings having the same aspect-ratios. Other non planar wing systems display an aerodynamic efficiency intermediate between ring wings and planar wings. Ring wing

Science of wings

The science behind how wings work can be complex and is one of the principal applications of the science of aerodynamics. However at the simplest level, both the upper and lower surfaces of a wing produces lift by deflecting air downward, which propels the flying body upward with an equal and opposite force (see Newton's Third Law). The air is deflected downwards because of Bernoulli's principle. This relates the pressure of air to its local velocity. If the velocity of the air changes as it flows around an object, such as a wing, the pressure of the air also changes. The shape and the angle of attack of the wing causes the air to flow faster above the wing than below, and so the pressure above the wing is less than below the wing. This pressure difference causes a force, called lift that acts at right angles to the air-flow. The science of wings applies in other areas beyond conventional fixed-wing aircraft, including:
- Helicopters which use a rotating wing with a variable pitch or angle to provide a directional force
- The space shuttle which uses its wings only for lift during its descent
- Formula One cars which use upside-down wings to give cars greater adhesion at high speeds
- Sailing boats which use sails as vertical wings with variable fullness and direction to move across water. Structures with the same purpose as wings, but designed to operate in liquid media, are generally called fins or hydroplanes, with hydrodynamics as the governing science. Applications arise in craft such as hydrofoils and submarines. Interestingly sailing boats use both fins and wings.

Evolution of wings in animals

Biologists believe that animal wings evolved at least four separate times, an example of convergent evolution. Insect wings are believed to have evolved about 300 million years ago, pterosaur wings about 225 million years ago, bird wings about 150 million years ago, and bat wings about 55 million years ago. Wings in these groups are analogous structures because they evolved independently rather than being passed from a common ancestor. See also flight.

External links

- [http://www.av8n.com/how/ An Excellent treatment of why and how wings generate lift]
- [http://www.npr.org/templates/story/story.php?storyId=3875411 Demystifying the Science of Flight] - Audio segment on NPR's Talk of the Nation Science Friday
- [http://www.grc.nasa.gov/WWW/K-12/airplane/short.html NASA's explanations and simulations]
- [http://aerodyn.org/Wings/ Advanced Topics in Aerodynamics] Wings for all speeds
- [http://www.nurseminerva.co.uk/adapt/evolutio.htm Evolution of flight] in animals
- [http://jef.raskincenter.org/published/coanda_effect.html Explanation invoking Coanda Effect] Category:Aerospace engineering Category:Aerodynamics Category:Aircraft components ja:翼

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

Speed of sound

:This page is about the physical constant that describe the speed of sound waves in a medium. For Coldplay single of their album, X&Y, see Speed of Sound (single). The speed of sound c (from Latin celeritas, "velocity") varies depending on the medium through which the sound waves pass. It is usually quoted in describing properties of substances (e.g. see the article on sodium). More commonly the term refers to the speed of sound in air. The speed varies depending on atmospheric conditions; the most important factor is the temperature. The humidity has very little effect on the speed of sound, while the static sound pressure (air pressure) has none. Sound travels slower with an increased altitude (elevation if you are on solid earth), primarily as a result of temperature and humidity changes. An approximate speed (in metres per second) can be calculated from: :

c_ = (3315 + (06 \cdot \theta)) \ \mathrm\,

where

\theta\,

(theta) is the temperature in degrees Celsius. A more accurate expression is :

c = \sqrt

where
- R (287.05 J/(kg·K) for air) is the universal gas constant (In this case, the gas constant R, which normally has units of J/(mol·K), is divided by the molar mass of air, as is common practice in aerodynamics)
- κ (kappa) is the adiabatic index (1.402 for air), sometimes noted γ
- T is the absolute temperature in kelvins. In the standard atmosphere: T₀ is 273.15 K (= 0 °C = 32 °F), giving a value of 331.5 m/s (= 1087.6 ft/s = 1193 km/h = 741.5 mph = 643.9 knots).
T₂₀ is 293.15 K (= 20 °C = 68 °F), giving a value of 343.4 m/s (= 1126.6 ft/s = 1236 km/h = 768.2 mph = 667.1 knots).
T₂₅ is 298.15 K (= 25 °C = 77 °F), giving a value of 346.3 m/s (= 1136.2 ft/s = 1246 km/h = 774.7 mph = 672.7 knots). In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure. Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere - actual conditions may vary. In a Non-Dispersive Medium – Sound speed is independent of frequency, therefore the speed of energy transport and sound propagation are the same. Air is a non-dispersive medium.
In a Dispersive Medium – Sound speed is a function of frequency. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at each its own phase speed, while the energy of the disturbance propagates at the group velocity. Water is an example of a dispersive medium. In general, the speed of sound c is given by :

c = \sqrt

where :C is a coefficient of stiffness :

\rho

is the density Thus the speed of sound increases with the stiffness of the material, and decreases with the density. In a fluid the only non-zero stiffness is to volumetric deformation (a fluid does not sustain shear forces). Hence the speed of sound in a fluid is given by :

c = \sqrt

where :K is the adiabatic bulk modulus For a gas, K is approximately given by :

K=\kappa \cdot p

where :κ is the adiabatic index, sometimes called γ. :p is the pressure. Thus, for a gas the speed of sound can be calculated using: :

c = \sqrt

which using the ideal gas law is identical to:

c = \sqrt

(Newton famously considered the speed of sound before most of the development of thermodynamics and so incorrectly used isothermal calculations instead of adiabatic. His result was missing the factor of κ but was otherwise correct.) In a solid, there is a non-zero stiffness both for volumetric and shear deformations. Hence, in a solid it is possible to generate sound waves with different velocities dependent on the deformation mode. In a solid rod (with thickness much smaller than the wavelength) the speed of sound is given by: :

c = \sqrt

where :E is Young's modulus :

\rho

(rho) is density Thus in steel the speed of sound is approximately 5100 m/s.
In a solid with lateral dimensions much larger than the wavelength, the sound velocity is higher. It is found be replacing Young's modulus with the plane wave modulus, which can be expressed in terms of the Young's modulus and Poisson's ratio as: :

M = E \frac

For air, see density of air. The speed of sound in water is of interest to those mapping the ocean floor. In saltwater, sound travels at about 1500 m/s and in freshwater 1435 m/s. These speeds vary due to pressure, depth, temperature, salinity and other factors. For general equations of state, if classical mechanics is used, the speed of sound

c

is given by :

c^2=\frac

where differentiation is taken with respect to adiabatic change. If relativistic effects are important, the speed of sound

S

is given by: :

S^2=c^2 \left. \frac \right|_

(Note that

e= \rho (c^2+e^C) \,

is the relativisic internal energy density; see relativistic Euler equations). This formula differs from the classical case in that

\rho

has been replaced by

e/c^2 \,

Table - Speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C

Mach number is the ratio of the object's speed to the speed of sound in air (medium).

Sound in solids

In solids, the velocity of sound depends on density of the material, not its temperature. Solid materials, such as steel, conduct sound much faster than air.

External links

- [http://www.sengpielaudio.com/calculator-speedsound.htm Calculation: Speed of sound in air and the temperature]
- [http://www.sengpielaudio.com/SpeedOfSoundPressure.pdf The speed of sound, the temperature, and ... not the air pressure]
- [http://www.pdas.com/atmos.htm Properties Of The U.S. Standard Atmosphere 1976] Category:Chemical properties Category:Fluid dynamics Category:Acoustics Category:Units of velocity ko:음속 ja:音速

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

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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

Алън Пейтън

Алън Стюарт Пейтън (английски: Alan Paton) е южноафрикански писател и създател на Южноафриканската либерална партия. Пейтън е известен със своята опозиция спрямо системата на апартейда.

Жизнен път

Пейтън е роден на 11 януари 1903 г. в Питърмарицбург, Натал. Баща му, Джеймс Пейтън, е шотландец, който емигрира в Южна Африка през 1895 г. Майка му, Юнис Уордър Джеймс Пейтън, е дъщеря на английски имигранти. Бащата на бъдещия писател е дълбоко вярващ християнин и очаква от сина си безприкословно да му се подчинява. Дисциплинарните му методи карат Алън да започне да презира и да се противопоставя открито на всички форми на авторитаризъм. Влиянието на баща му обаче не било само в отрицателна посока. Той научил сина си да обича книгите и природата. След като завършва Марицбургския колеж през 1918 г., Пейтън продължава образованието си в Университета на Натал, където завършва с отличие в областта на физиката. След това става учител по наука през 1925 г. Той учителства в гимназията в Иксопо три години, но след това се мести в Питърмарицбург за да преподава в Марицбургския колеж. През 1928 г. Пейтън се жени за Дорис Олив Франсис, и след две години му се ражда първороден син, Дейвид. Вторият му син, Йонатан, е роден през 1936 г. Дори в началото на своята кариера Пейтър показва заинтересованост спрямо расовите отношения, като се присъединява

Drag

See also

Drag (disambiguation)

Gas

Properties of a gas

Etymology

See also

Hydrodynamics

See also

Force

Elementary concepts

Quantitative definition

Types of force

Properties of force

Forces in theory

Units of measurement

Non-SI units of force and mass

Conversions

Forces in everyday life

Forces in the laboratory

Founding experiments

Instruments to measure forces

History

See also

References

External links

Thrust

Examples

See also

Lift-induced drag

Aspect Ratio

Wing Planform

Coefficient of Lift

See also

Wave drag

Overview

Research

Reduction of drag

Other drag reduction methods

Skin friction

Wing

Use

Artificial wings

Terms used to describe aeroplane wings

Design features

Wing types

Science of wings

Evolution of wings in animals

External links

Wave drag

Overview

Research

Reduction of drag

Other drag reduction methods

Speed of sound

Table - Speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C

Sound in solids

External links

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

C_d in automobiles

C_dA