Accuracy and precision
Precision is a description of random errors, a measure of statistical variability. The two concepts are independent of other, so a particular set of data can be said to be either accurate, or precise. In the fields of science and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantitys true value. The precision of a measurement system, related to reproducibility and repeatability, is the degree to which repeated measurements under unchanged conditions show the same results. Although the two words precision and accuracy can be synonymous in colloquial use, they are contrasted in the context of the scientific method. A measurement system can be accurate but not precise, precise but not accurate, for example, if an experiment contains a systematic error, increasing the sample size generally increases precision but does not improve accuracy. The result would be a consistent yet inaccurate string of results from the flawed experiment, eliminating the systematic error improves accuracy but does not change precision. A measurement system is considered if it is both accurate and precise.
Related terms include bias and error, the terminology is applied to indirect measurements—that is, values obtained by a computational procedure from observed data. Statistical literature prefers to use the terms bias and variability instead of accuracy and precision, bias is the amount of inaccuracy and variability is the amount of imprecision. In military terms, accuracy refers primarily to the accuracy of fire, ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the true value. The accuracy and precision of a measurement process is established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units and maintained by national organizations such as the National Institute of Standards. This applies when measurements are repeated and averaged, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements.
With regard to accuracy we can distinguish, the difference between the mean of the measurements and the value, the bias. Establishing and correcting for bias is necessary for calibration, the combined effect of that and precision. A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures, when not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m, while a recording of 8,436 m would imply a margin of error of 0.5 m
The escape velocity from Earth is about 11.186 km/s at the surface. More generally, escape velocity is the speed at which the sum of a kinetic energy. With escape velocity in a direction pointing away from the ground of a massive body, once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. When given a speed V greater than the speed v e. In these equations atmospheric friction is not taken into account, escape velocity is only required to send a ballistic object on a trajectory that will allow the object to escape the gravity well of the mass M. The existence of escape velocity is a consequence of conservation of energy, by adding speed to the object it expands the possible places that can be reached until with enough energy they become infinite. For a given gravitational potential energy at a position, the escape velocity is the minimum speed an object without propulsion needs to be able to escape from the gravity. Escape velocity is actually a speed because it does not specify a direction, no matter what the direction of travel is, the simplest way of deriving the formula for escape velocity is to use conservation of energy.
Imagine that a spaceship of mass m is at a distance r from the center of mass of the planet and its initial speed is equal to its escape velocity, v e. At its final state, it will be a distance away from the planet. The same result is obtained by a calculation, in which case the variable r represents the radial coordinate or reduced circumference of the Schwarzschild metric. All speeds and velocities measured with respect to the field, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point. In common usage, the point is on the surface of a planet or moon. On the surface of the Earth, the velocity is about 11.2 km/s. However, at 9,000 km altitude in space, it is less than 7.1 km/s. The escape velocity is independent of the mass of the escaping object and it does not matter if the mass is 1 kg or 1,000 kg, what differs is the amount of energy required. For an object of mass m the energy required to escape the Earths gravitational field is GMm / r, a related quantity is the specific orbital energy which is essentially the sum of the kinetic and potential energy divided by the mass.
An object has reached escape velocity when the orbital energy is greater or equal to zero
For example, the path of an object launched from Earth that reaches 100 km above sea level, and falls back to Earth, is considered a sub-orbital spaceflight. Some sub-orbital flights have been undertaken to test spacecraft and launch vehicles intended for orbital spaceflight, other vehicles are specifically designed only for sub-orbital flight, examples include manned vehicles such as the X-15 and SpaceShipOne, and unmanned ones such as ICBMs and sounding rockets. Flights which attain sufficient velocity to go into low Earth orbit, examples of this include Yuri Gagarins Vostok 1, and flights of the Fractional Orbital Bombardment System. Usually a rocket is used, but experimental sub-orbital spaceflight has achieved with a space gun. By one definition a sub-orbital spaceflight reaches a higher than 100 km above sea level. The US military and NASA award astronaut wings to those flying above 50 mi, during freefall the trajectory is part of an elliptic orbit as given by the orbit equation. The perigee distance is less than the radius of the Earth R including atmosphere, hence the ellipse intersects the Earth, the major axis is vertical, the semi-major axis a is more than R/2.
The specific orbital energy ϵ is given by, ε = − μ2 a > − μ R where μ is the standard gravitational parameter, to minimize the required delta-v, the high-altitude part of the flight is made with the rockets off. The maximum speed in a flight is attained at the lowest altitude of this free-fall trajectory, if ones goal is simply to reach space, for example in competing for the Ansari X Prize, horizontal motion is not needed. In this case the lowest required delta-v, to reach 100 km altitude, is about 1.4 km/s, for sub-orbital spaceflights covering a horizontal distance the maximum speed and required delta-v are in between those of a vertical flight and a LEO. The maximum speed at the ends of the trajectory are now composed of a horizontal. The higher the horizontal distance covered, the greater both speeds will be, for the V-2 rocket, just reaching space but with a range of about 330 km, the maximum speed was 1.6 km/s. Scaled Composites SpaceShipTwo which is under development will have a similar free-fall orbit, for larger ranges, due to the elliptic orbit the maximum altitude can even be considerably more than for a LEO.
It should be noted that any spaceflight that returns to the surface, including sub-orbital ones, the speed at the start of the reentry is basically the maximum speed of the flight. The aerodynamic heating caused will vary accordingly, it is less for a flight with a maximum speed of only 1 km/s than for one with a maximum speed of 7 or 8 km/s. Let θ be half the angle that the projectile is to go around the earth, the minimum-delta-v trajectory corresponds to an ellipse with one focus at the centre of the earth and the other at the point halfway between the launch point and the destination point. Longer ranges will have lower apogees in the minimal-delta-v solution and we see that the Δv increases with range, leveling off at 7.9 km/s as the range approaches 20000 km. The minimum-delta-v trajectory for going halfway around the world corresponds to a circular orbit just above the surface, see lower for the time of flight
International Standard Book Number
The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay.
The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces.
Separating the parts of a 10-digit ISBN is done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
The Magnus effect is the commonly observed effect in which a spinning ball curves away from its principal flight path. It is important in many ball sports and it affects spinning missiles, and has some engineering uses, for instance in the design of rotor ships and Flettner aeroplanes. In terms of games, topspin is defined as spin about an axis perpendicular to the direction of travel. Under the Magnus effect, topspin produces a downward swerve of a ball, greater than would be produced by gravity alone. Likewise side-spin causes swerve to either side as seen during some baseball pitches, the overall behaviour is similar to that around an aerofoil with a circulation which is generated by the mechanical rotation, rather than by airfoil action. The Magnus effect is named after Heinrich Gustav Magnus, the German physicist who investigated it, the force on a rotating cylinder is known as Kutta–Joukowski lift, after Martin Wilhelm Kutta and Nikolai Zhukovsky, who first analyzed the effect. The body pushes the air down, and the air pushes the body upward, as a particular case, a lifting force is accompanied by a downward deflection of the air-flow.
It is a deflection in the fluid flow, aft of the body. In fact there are ways in which the rotation might cause such a deflection. By far the best way to know what happens in typical cases is by wind tunnel experiments. Lyman Briggs made a wind tunnel study of the Magnus effect on baseballs. The studies show a turbulent wake behind the spinning ball, the wake is to be expected and is the cause of aerodynamic drag. However there is an angular deflection in the wake and the deflection is in the direction of the spin. The process by which a turbulent wake develops aft of a body in an air-flow is complex and it is found that the thin boundary layer detaches itself from the body at some point and this is where the wake begins to develop. The boundary layer itself may be turbulent or not, this has a significant effect on the wake formation, quite small variations in the surface conditions of the body can influence the onset of wake formation and thereby have a marked effect on the downstream flow pattern.
The influence of the rotation is of this kind. It is said that Magnus himself wrongly postulated a theoretical effect with laminar flow due to skin friction, such effects are physically possible but slight in comparison to what is produced in the Magnus effect proper. In some circumstances the causes of the Magnus effect can produce a deflection opposite to that of the Magnus effect, the diagram at the head of this article shows lift being produced on a back-spinning ball
In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two layers or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are independent of velocity. Drag force is proportional to the velocity for a laminar flow, even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity. Drag forces always decrease fluid velocity relative to the object in the fluids path. In the case of viscous drag of fluid in a pipe, in physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters. Types of drag are generally divided into the categories, parasitic drag, consisting of form drag, skin friction, interference drag, lift-induced drag. The phrase parasitic drag is used in aerodynamics, since for lifting wings drag it is in general small compared to lift. For flow around bluff bodies and interference drags often dominate, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in aviation or in the design of semi-planing or planing hulls.
Wave drag occurs either when an object is moving through a fluid at or near the speed of sound or when a solid object is moving along a fluid boundary. Drag depends on the properties of the fluid and on the size, shape, at low R e, C D is asymptotically proportional to R e −1, which means that the drag is linearly proportional to the speed. At high R e, C D is more or less constant, the graph to the right shows how C D varies with R e for the case of a sphere. As mentioned, the equation with a constant drag coefficient gives the force experienced by an object moving through a fluid at relatively large velocity. This is called quadratic drag, the equation is attributed to Lord Rayleigh, who originally used L2 in place of A. Sometimes a body is a composite of different parts, each with a different reference areas, in the case of a wing the reference areas are the same and the drag force is in the same ratio to the lift force as the ratio of drag coefficient to lift coefficient. Therefore, the reference for a wing is often the area rather than the frontal area.
For an object with a surface, and non-fixed separation points—like a sphere or circular cylinder—the drag coefficient may vary with Reynolds number Re. For an object with well-defined fixed separation points, like a disk with its plane normal to the flow direction
In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object.
Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules.
Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
In firearms, rifling consists of helical grooves in the internal surface of a guns barrel, which impart a spin to a projectile around its long axis. This spin serves to stabilize the projectile, improving its aerodynamic stability. Rifling is often described by its twist rate, which indicates the distance the rifling takes to complete one revolution, such as 1 turn in 10 inches. A shorter distance indicates a faster twist, meaning that for a given velocity the projectile will be rotating at a spin rate. Barrels intended for long, small-diameter bullets, such as the ultra-low-drag, 80-grain 0.223 inch bullets, extremely long projectiles such as flechettes may require high twist rates, these projectiles must be inherently stable, and are often fired from a smoothbore barrel. Muskets were smoothbore, large caliber weapons using ball-shaped ammunition fired at low velocity. Due to the high cost and great difficulty of manufacturing, and the need to load readily from the muzzle. Consequently, on firing the ball bounced off the sides of the barrel when fired, barrel rifling was invented in Augsburg, Germany in 1498.
In 1520 August Kotter, an armourer of Nuremberg, Germany improved upon this work, though true rifling dates from the mid-16th century, it did not become commonplace until the nineteenth century. The most successful weapons using rifling with black powder were breech loaders such as the Queen Anne pistol, the grooves most commonly used in modern rifling have fairly sharp edges. More recently, polygonal rifling, a throwback to the earliest types of rifling, has become popular, polygonal barrels tend to have longer service lives because the reduction of the sharp edges of the land reduces erosion of the barrel. Supporters of polygonal rifling claim higher velocities and greater accuracy, polygonal rifling is currently seen on pistols from CZ, Heckler & Koch, Glock and Kahr Arms, as well as the Desert Eagle. Such guns have achieved significant increases in velocity and range. Examples include the South African G5 and the German PzH2000, gain-twist rifling begins with very little change in the projectiles angular momentum during the first few inches of bullet travel after ignition during the transition from chamber to throat.
This enables the bullet to remain undisturbed and trued to the case mouth. After engaging the rifling the bullet is progressively subjected to accelerated angular momentum as burning powder propels it down the barrel. By only gradually increasing the rate, torque is spread along a much longer section of barrel. Gain-twist rifling was used as early as the American Civil War, colt Army and Navy revolvers both employed gain-twist rifling
A projectile is any object thrown into space by the exertion of a force. Although any object in motion through space may be called a projectile, mathematical equations of motion are used to analyze projectile trajectory. Blowguns and pneumatic rifles use compressed gases, while most other guns and cannons utilize expanding gases liberated by sudden chemical reactions, light-gas guns use a combination of these mechanisms. Railguns utilize electromagnetic fields to provide a constant acceleration along the length of the device. Some projectiles provide propulsion during flight by means of an engine or jet engine. In military terminology, a rocket is unguided, while a missile is guided, note the two meanings of rocket, an ICBM is a guided missile with a rocket engine. An explosion, whether or not by a weapon, causes the debris to act as high velocity projectiles. An explosive weapon, or device may be designed to produce high velocity projectiles by the break-up of its casing. Many projectiles, e. g. shells, may carry a charge or another chemical or biological substance.
Aside from explosive payload, a projectile can be designed to cause damage, e. g. fire. Typical kinetic energy weapons are blunt projectiles such as rocks and round shots, pointed ones such as arrows, among projectiles that do not contain explosives are those launched from railguns and mass drivers, as well as kinetic energy penetrators. Other types of weapons are accelerated over time by a rocket engine. In either case, it is the energy of the projectile that destroys its target. Some kinetic weapons for targeting objects in spaceflight are anti-satellite weapons, since in order to reach an object in orbit it is necessary to attain an extremely high velocity, their released kinetic energy alone is enough to destroy their target, explosives are not necessary. For example, the energy of TNT is 4.6 MJ/kg, and this saves costly weight and there is no detonation to be precisely timed. This method, requires direct contact with the target, some hit-to-kill warheads are additionally equipped with an explosive directional warhead to enhance the kill probability.
With regard to weapons, the Arrow missile and MIM-104 Patriot PAC-2 have explosives, while the Kinetic Energy Interceptor, Lightweight Exo-Atmospheric Projectile. A kinetic projectile can be dropped from aircraft and this is applied by replacing the explosives of a regular bomb with a non-explosive material, for a precision hit with less collateral damage
Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre, three dimensional mathematical shapes are assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, Volumes of a complicated shape can be calculated by integral calculus if a formula exists for the shapes boundary. Where a variance in shape and volume occurs, such as those that exist between different human beings, these can be calculated using techniques such as the Body Volume Index. One-dimensional figures and two-dimensional shapes are assigned zero volume in the three-dimensional space, the volume of a solid can be determined by fluid displacement. Displacement of liquid can be used to determine the volume of a gas, the combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the other and the volume is not additive.
In differential geometry, volume is expressed by means of the volume form, in thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure. Any unit of length gives a unit of volume, the volume of a cube whose sides have the given length. For example, a cubic centimetre is the volume of a cube whose sides are one centimetre in length, in the International System of Units, the standard unit of volume is the cubic metre. The metric system includes the litre as a unit of volume, thus 1 litre =3 =1000 cubic centimetres =0.001 cubic metres, so 1 cubic metre =1000 litres. Small amounts of liquid are often measured in millilitres, where 1 millilitre =0.001 litres =1 cubic centimetre. Capacity is defined by the Oxford English Dictionary as the applied to the content of a vessel, and to liquids, grain, or the like. Capacity is not identical in meaning to volume, though closely related, Units of capacity are the SI litre and its derived units, and Imperial units such as gill, pint and others.
Units of volume are the cubes of units of length, in SI the units of volume and capacity are closely related, one litre is exactly 1 cubic decimetre, the capacity of a cube with a 10 cm side. In other systems the conversion is not trivial, the capacity of a fuel tank is rarely stated in cubic feet, for example. The density of an object is defined as the ratio of the mass to the volume, the inverse of density is specific volume which is defined as volume divided by mass. Specific volume is an important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied
In the taxonomies of artillery pieces used by European armies in the 17th to 20th centuries, the howitzer stood between the gun and the mortar. Howitzers, like other artillery equipment, are organized in groups called batteries. The English word howitzer comes from the Czech word houfnice, from houf, haufen, sometimes in the compound Gewalthaufen, designated a pike square formation in German. This is particularly true in the forces of the United States. Because of this practice, the howitzer is used in some armies as a generic term for any kind of artillery piece that is designed to attack targets using indirect fire. Thus, artillery pieces that bear resemblance to howitzers of earlier eras are now described as howitzers. Most other armies in the reserve the word howitzer for guns with barrel lengths 15 to 25 times their caliber. The British had a method of nomenclature. In the 18th century, they adopted projectile weight for guns replacing the old naming system of culverin, mortars had been categorized by calibre in inches in the 17th century and this was inherited by howitzers.
The modern howitzers were invented in Sweden towards the end of the 17th century, originally intended for use in siege warfare, they were particularly useful for delivering cast-iron shells filled with gunpowder or incendiary materials into the interior of fortifications. In the middle of the 18th century, a number of European armies began to introduce howitzers that were enough to accompany armies in the field. Though usually fired at the high angles of fire used by contemporary siege howitzers. Rather, as the guns of the day were usually restricted to inert projectiles. Many, for the sake of simplicity and rapidity of fire, the Abus gun was an early form of howitzer in the Ottoman Empire. In 1758 the Russian Empire introduced a type of howitzer, with a conical chamber, called a licorne. The most famous of these gun-howitzers was the Napoleon 12-pounder, a weapon of French design that saw service in the American Civil War. The longest-serving artillery piece of the 19th century was the mountain howitzer, in 1859, the armies of Europe began to rearm field batteries with rifled field guns.
These new field pieces used cylindrical projectiles that, while smaller in caliber than the spherical shells of smoothbore field howitzers, their greater range let them create many of the same effects that previously required the sharply curved trajectories of smoothbore field howitzers
A gun barrel is a part of firearms and artillery pieces. The hollow interior of the barrel is called the bore, a gun barrel must be able to hold in the expanding gas produced by the propellants to ensure that optimum muzzle velocity is attained by the projectile as it is being pushed out by the expanding gas. Modern small arms barrels are made of known and tested to withstand the pressures involved. Artillery pieces are made by various techniques providing reliably sufficient strength, early firearms were muzzle-loading, with powder, and shot loaded from the muzzle, capable of only a low rate of fire. During the 19th century effective mechanical locks were invented that sealed a breech-loading weapon against the escape of propellant gases, the early Chinese, the inventors of gunpowder, used bamboo, a naturally tubular stalk, as the first barrels in gunpowder projectile weapons. Early European guns were made of iron, usually with several strengthening bands of the metal wrapped around circular wrought iron rings.
The Chinese were the first to master cast-iron cannon barrels, early cannon barrels were very thick for their caliber. Bore evacuator Bore snake Cannon Muzzle Polygonal rifling Rifling Slug barrel Smoothbore