title: Stirling engine

text: Robert Stirling is considered one of the fathers of hot air engines, notwithstanding some earlier predecessors—notably Guillaume Amontons, who succeeded in building, in 1699, the first working hot air engine.


title: Stirling engine

text: Amontons was later followed by Sir George Cayley. This engine type was of those in which the fire is enclosed, and fed by air pumped in beneath the grate in sufficient quantity to maintain combustion, while by far the largest portion of the air enters above the fire, to be heated and expanded; the whole, together with the products of combustion, then acts on the piston, and passes through the working cylinder; and the operation being one of simple mixture only, no heating surface of metal is required, the air to be heated being brought into immediate contact with the fire.


title: Stirling engine

text: Stirling came up with a first air engine in 1816. The principle of the Stirling Air Engine differs from that of Sir George Cayley (1807), in which the air is forced through the furnace and exhausted, whereas in Stirling's engine the air works in a closed circuit. The inventor devoted most of his attention to that.


title: Stirling engine

text: A engine, built in 1818 for pumping water at an Ayrshire quarry, continued to work for some time, until a careless attendant allowed the heater to become overheated. This experiment proved to the inventor that, owing to the low working pressure obtainable, the engine could only be adapted to small powers for which there was, at that time, no demand.


title: Stirling engine

text: The Stirling 1816 patent was also about an "Economiser", which is the predecessor of the regenerator. In this patent (# 4081) he describes the "economiser" technology and several applications where such technology can be used. Out of them came a new arrangement for a hot air engine.


title: Stirling engine

text: Stirling patented a second hot air engine, together with his brother James, in 1827. They inverted the design so that the hot ends of the displacers were underneath the machinery, and they added a compressed air pump so the air within could be increased in pressure to around .


title: Stirling engine

text: The two Stirling brothers were followed shortly after (1828) by Parkinson & Crossley and Arnott in 1829.


title: Stirling engine

text: These precursors, to whom Ericsson should be added, have brought to the world the hot air engine technology and its enormous advantages over the steam engine. Each of them came with his own specific technology, and although the Stirling engine and the Parkinson & Crossley engines were quite similar, Robert Stirling distinguished himself by inventing the regenerator.


title: Stirling engine

text: Parkinson and Crosley introduced the principle of using air of greater density than that of the atmosphere, and so obtained an engine of greater power in the same compass. James Stirling followed this same idea when he built the famous Dundee engine.


title: Stirling engine

text: The Stirling patent of 1827 was the base of the Stirling third patent of 1840. The changes from the 1827 patent were minor but essential, and this third patent led to the Dundee engine.


title: Stirling engine

text: James Stirling presented his engine to the Institution of Civil Engineers in 1845. The first engine of this kind which, after various modifications, was efficiently constructed and heated, had a cylinder of in diameter, with a length of stroke of , and made 40 strokes or revolutions in a minute (40 rpm). This engine moved all the machinery at the Dundee Foundry Company's works for eight or ten months, and was previously found capable of raising 320,000 kg (700,000 lbs) 60 cm (2 ft) in a minute, a power of approximately .


title: Stirling engine

text: Finding this power insufficient for their works, the Dundee Foundry Company erected the second engine, with a cylinder of in diameter, a stroke of , and making 28 strokes in a minute. When this engine had been in continual operation for upwards of two years, it had not only performed the work of the foundry in the most satisfactory manner, but had been tested (by a friction brake on a third mover) to the extent of lifting nearly , a power of approximately .


title: Stirling engine

text: The Stirling engine (or Stirling's air engine as it was known at the time) was invented and patented in 1816. It followed earlier attempts at making an air engine but was probably the first put to practical use when, in 1818, an engine built by Stirling was employed pumping water in a quarry. The main subject of Stirling's original patent was a heat exchanger, which he called an "economiser" for its enhancement of fuel economy in a variety of applications. The patent also described in detail the employment of one form of the economiser in his unique closed-cycle air engine design in which application it is now generally known as a "regenerator". Subsequent development by Robert Stirling and his brother James, an engineer, resulted in patents for various improved configurations of the original engine including pressurization, which by 1843, had sufficiently increased power output to drive all the machinery at a Dundee iron foundry.


title: Stirling engine

text: A paper presented by James Stirling in June 1845 to the Institution of Civil Engineers stated that his aims were not only to save fuel but also to create a safer alternative to the steam engines of the time, whose boilers frequently exploded, causing many injuries and fatalities. This has however been disputed.


title: Stirling engine

text: The need for Stirling engines to run at very high temperatures to maximize power and efficiency exposed limitations in the materials of the day, and the few engines that were built in those early years suffered unacceptably frequent failures (albeit with far less disastrous consequences than boiler explosions). For example, the Dundee foundry engine was replaced by a steam engine after three hot cylinder failures in four years.


title: Stirling engine

text: Subsequent to the replacement of the Dundee foundry engine there is no record of the Stirling brothers having any further involvement with air engine development, and the Stirling engine never again competed with steam as an industrial scale power source. (Steam boilers were becoming safer, e.g. the Hartford Steam Boiler and steam engines more efficient, thus presenting less of a target for rival prime movers). However, beginning about 1860, smaller engines of the Stirling/hot air type were produced in substantial numbers for applications in which reliable sources of low to medium power were required, such as pumping air for church organs or raising water. These smaller engines generally operated at lower temperatures so as not to tax available materials, and so were relatively inefficient. Their selling point was that unlike steam engines, they could be operated safely by anybody capable of managing a fire. The 1906 Rider-Ericsson Engine Co. catalog claimed that "any gardener or ordinary domestic can operate these engines and no licensed or experienced engineer is required". Several types remained in production beyond the end of the century, but apart from a few minor mechanical improvements the design of the Stirling engine in general stagnated during this period.


title: Stirling engine

text: During the early part of the 20th century, the role of the Stirling engine as a "domestic motor" was gradually taken over by electric motors and small internal combustion engines. By the late 1930s, it was largely forgotten, only produced for toys and a few small ventilating fans.


title: Stirling engine

text: Around that time, Philips was seeking to expand sales of its radios into parts of the world where grid electricity and batteries were not consistently available. Philips' management decided that offering a low-power portable generator would facilitate such sales and asked a group of engineers at the company's research lab in Eindhoven to evaluate alternative ways of achieving this aim. After a systematic comparison of various prime movers, the team decided to go forward with the Stirling engine, citing its quiet operation (both audibly and in terms of radio interference) and ability to run on a variety of heat sources (common lamp oil – "cheap and available everywhere" – was favored). They were also aware that, unlike steam and internal combustion engines, virtually no serious development work had been carried out on the Stirling engine for many years and asserted that modern materials and know-how should enable great improvements.


title: Stirling engine

text: By 1951, the 180/200 W generator set designated MP1002CA (known as the "Bungalow set") was ready for production and an initial batch of 250 was planned, but soon it became clear that they could not be made at a competitive price. Additionally, the advent of transistor radios and their much lower power requirements meant that the original reason for the set was disappearing. Approximately 150 of these sets were eventually produced. Some found their way into university and college engineering departments around the world, giving generations of students a valuable introduction to the Stirling engine; a letter dated March 1961 from Research and Control Instruments Ltd. London WC1 to North Devon Technical College, offering "remaining stocks... to institutions such as yourselves... at a special price of £75 net".


title: Stirling engine

text: In parallel with the Bungalow set, Philips developed experimental Stirling engines for a wide variety of applications and continued to work in the field until the late 1970s, but only achieved commercial success with the "reversed Stirling engine" cryocooler. However, they filed a large number of patents and amassed a wealth of information, which they licensed to other companies and which formed the basis of much of the development work in the modern era.


title: Stirling engine

text: In 1996, the Swedish navy commissioned three Gotland-class submarines. On the surface, these boats are propelled by marine diesel engines. However, when submerged, they use a Stirling-driven generator developed by Swedish shipbuilder Kockums to recharge batteries and provide electrical power for propulsion. A supply of liquid oxygen is carried to support burning of diesel fuel to power the engine. Stirling engines are also fitted to the Swedish Södermanland-class submarines, the Archer-class submarines in service in Singapore and, license-built by Kawasaki Heavy Industries for the Japanese Sōryū-class submarines. In a submarine application, the Stirling engine offers the advantage of being exceptionally quiet when running.


title: Stirling engine

text: By the turn of the 21st century, Stirling engines were used in the dish version of Concentrated Solar Power systems. A mirrored dish similar to a very large satellite dish directs and concentrates sunlight onto a thermal receiver, which absorbs and collects the heat and using a fluid transfers it into the Stirling engine. The resulting mechanical power is then used to run a generator or alternator to produce electricity.


title: Stirling engine

text: The core component of micro combined heat and power (CHP) units can be formed by a Stirling cycle engine, as they are more efficient and safer than a comparable steam engine. By 2003, CHP units were being commercially installed in domestic applications.


title: Stirling engine

text: In 2013, an article was published about scaling laws of free-piston Stirling engines based on six characteristic dimensionless groups.


title: Stirling engine

text: Robert Stirling patented the first practical example of a closed-cycle hot air engine in 1816, and it was suggested by Fleeming Jenkin as early as 1884 that all such engines should therefore generically be called Stirling engines. This naming proposal found little favour, and the various types on the market continued to be known by the name of their individual designers or manufacturers, e.g., Rider's, Robinson's, or Heinrici's (hot) air engine. In the 1940s, the Philips company was seeking a suitable name for its own version of the 'air engine', which by that time had been tested with working fluids other than air, and decided upon 'Stirling engine' in April 1945. However, nearly thirty years later, Graham Walker still had cause to bemoan the fact such terms as "hot air engine" remained interchangeable with "Stirling engine", which itself was applied widely and indiscriminately, a situation that continues.


title: Stirling engine

text: Like the steam engine, the Stirling engine is traditionally classified as an external combustion engine, as all heat transfers to and from the working fluid take place through a solid boundary (heat exchanger) thus isolating the combustion process and any contaminants it may produce from the working parts of the engine. This contrasts with an internal combustion engine where heat input is by combustion of a fuel within the body of the working fluid. Most of the many possible implementations of the Stirling engine fall into the category of reciprocating piston engine.


title: Stirling engine

text: The engine is designed so the working gas is generally compressed in the colder portion of the engine and expanded in the hotter portion resulting in a net conversion of heat into work. An internal regenerative heat exchanger increases the Stirling engine's thermal efficiency compared to simpler hot air engines lacking this feature.


title: Stirling engine

text: The Stirling engine uses the temperature difference between its hot end and cold end to establish a cycle of a fixed mass of gas, heated and expanded, and cooled and compressed, thus converting thermal energy into mechanical energy. The greater the temperature difference between the hot and cold sources, the greater the thermal efficiency. The maximum theoretical efficiency is equivalent to that of the Carnot cycle, but the efficiency of real engines is less than this value because of friction and other losses.


title: Stirling engine

text: Since the Stirling engine is a closed cycle, it contains a fixed mass of gas called the "working fluid", most commonly air, hydrogen or helium. In normal operation, the engine is sealed and no gas enters or leaves; no valves are required, unlike other types of piston engines. The Stirling engine, like most heat engines, cycles through four main processes: cooling, compression, heating, and expansion. This is accomplished by moving the gas back and forth between hot and cold heat exchangers, often with a regenerator between the heater and cooler. The hot heat exchanger is in thermal contact with an external heat source, such as a fuel burner, and the cold heat exchanger is in thermal contact with an external heat sink, such as air fins. A change in gas temperature causes a corresponding change in gas pressure, while the motion of the piston makes the gas alternately expand and compress.


title: Stirling engine

text: The gas follows the behaviour described by the gas laws that describe how a gas's pressure, temperature, and volume are related. When the gas is heated, the pressure rises (because it is in a sealed chamber) and this pressure then acts on the power piston to produce a power stroke. When the gas is cooled the pressure drops and this drop means that the piston needs to do less work to compress the gas on the return stroke. The difference in work between the strokes yields a net positive power output.


title: Stirling engine

text: When one side of the piston is open to the atmosphere, the operation is slightly different. As the sealed volume of working gas comes in contact with the hot side, it expands, doing work on both the piston and on the atmosphere. When the working gas contacts the cold side, its pressure drops below atmospheric pressure and the atmosphere pushes on the piston and does work on the gas.


title: Stirling engine

text: As a consequence of closed-cycle operation, the heat driving a Stirling engine must be transmitted from a heat source to the working fluid by heat exchangers and finally to a heat sink. A Stirling engine system has at least one heat source, one heat sink and up to five heat exchangers. Some types may combine or dispense with some of these.


title: Stirling engine

text: The heat source may be provided by the combustion of a fuel and, since the combustion products do not mix with the working fluid and hence do not come into contact with the internal parts of the engine, a Stirling engine can run on fuels that would damage other engines types' internals, such as landfill gas, which may contain siloxane that could deposit abrasive silicon dioxide in conventional engines.


title: Stirling engine

text: Other suitable heat sources include concentrated solar energy, geothermal energy, nuclear energy, waste heat and bioenergy. If solar power is used as a heat source, regular solar mirrors and solar dishes may be utilised. The use of Fresnel lenses and mirrors has also been advocated, for example in planetary surface exploration. Solar powered Stirling engines are increasingly popular as they offer an environmentally sound option for producing power while some designs are economically attractive in development projects.


title: Stirling engine

text: Designing Stirling engine heat exchangers is a balance between high heat transfer with low viscous pumping losses, and low dead space (unswept internal volume). Engines that operate at high powers and pressures require that heat exchangers on the hot side be made of alloys that retain considerable strength at high temperatures and that don't corrode or creep.


title: Stirling engine

text: In small, low power engines the heat exchangers may simply consist of the walls of the respective hot and cold chambers, but where larger powers are required a greater surface area is needed to transfer sufficient heat. Typical implementations are internal and external fins or multiple small bore tubes for the hot side, and a cooler using a liquid (like water) for the cool side.


title: Stirling engine

text: In a Stirling engine, the regenerator is an internal heat exchanger and temporary heat store placed between the hot and cold spaces such that the working fluid passes through it first in one direction then the other, taking heat from the fluid in one direction, and returning it in the other. It can be as simple as metal mesh or foam, and benefits from high surface area, high heat capacity, low conductivity and low flow friction. Its function is to retain within the system that heat which would otherwise be exchanged with the environment at temperatures intermediate to the maximum and minimum cycle temperatures, thus enabling the thermal efficiency of the cycle (though not of any practical engine) to approach the limiting Carnot efficiency.


title: Stirling engine

text: The primary effect of regeneration in a Stirling engine is to increase the thermal efficiency by 'recycling' internal heat which would otherwise pass through the engine irreversibly. As a secondary effect, increased thermal efficiency yields a higher power output from a given set of hot and cold end heat exchangers. These usually limit the engine's heat throughput. In practice this additional power may not be fully realized as the additional "dead space" (unswept volume) and pumping loss inherent in practical regenerators reduces the potential efficiency gains from regeneration.


title: Stirling engine

text: The design challenge for a Stirling engine regenerator is to provide sufficient heat transfer capacity without introducing too much additional internal volume ('dead space') or flow resistance. These inherent design conflicts are one of many factors that limit the efficiency of practical Stirling engines. A typical design is a stack of fine metal wire meshes, with low porosity to reduce dead space, and with the wire axes perpendicular to the gas flow to reduce conduction in that direction and to maximize convective heat transfer.


title: Stirling engine

text: The regenerator is the key component invented by Robert Stirling, and its presence distinguishes a true Stirling engine from any other closed-cycle hot air engine. Many small 'toy' Stirling engines, particularly low-temperature difference (LTD) types, do not have a distinct regenerator component and might be considered hot air engines; however a small amount of regeneration is provided by the surface of the displacer itself and the nearby cylinder wall, or similarly the passage connecting the hot and cold cylinders of an alpha configuration engine.


title: Stirling engine

text: The larger the temperature difference between the hot and cold sections of a Stirling engine, the greater the engine's efficiency. The heat sink is typically the environment the engine operates in, at ambient temperature. In the case of medium- to high-power engines, a radiator is required to transfer the heat from the engine to the ambient air. Marine engines have the advantage of using cool ambient sea, lake, or river water, which is typically cooler than ambient air. In the case of combined heat and power systems, the engine's cooling water is used directly or indirectly for heating purposes, raising efficiency.


title: Stirling engine

text: Alternatively, heat may be supplied at ambient temperature and the heat sink maintained at a lower temperature by such means as cryogenic fluid (see Liquid nitrogen economy) or iced water.


title: Stirling engine

text: The displacer is a special-purpose piston, used in Beta and Gamma type Stirling engines, to move the working gas back and forth between the hot and cold heat exchangers. Depending on the type of engine design, the displacer may or may not be sealed to the cylinder; i.e., it may be a loose fit within the cylinder, allowing the working gas to pass around it as it moves to occupy the part of the cylinder beyond. The Alpha type engine has a high stress on the hot side, that's why so few inventors started to use a hybrid piston for that side. The hybrid piston has a sealed part as a normal Alpha type engine, but it has a connected displacer part with smaller diameter as the cylinder around that. The compression ratio is a bit smaller than in the original Alpha type engines, but the stress factor is pretty low on the sealed parts.


title: Stirling engine

text: The three major types of Stirling engines are distinguished by the way they move the air between the hot and cold areas:


title: Stirling engine

text: An alpha Stirling contains two power pistons in separate cylinders, one hot and one cold. The hot cylinder is situated inside the high-temperature heat exchanger and the cold cylinder is situated inside the low-temperature heat exchanger. This type of engine has a high power-to-volume ratio but has technical problems because of the usually high temperature of the hot piston and the durability of its seals. In practice, this piston usually carries a large insulating head to move the seals away from the hot zone at the expense of some additional dead space. The crank angle has a major effect on efficiency and the best angle frequently must be found experimentally. An angle of 90° frequently locks.


title: Stirling engine

text: A beta Stirling has a single power piston arranged within the same cylinder on the same shaft as a displacer piston. The displacer piston is a loose fit and does not extract any power from the expanding gas but only serves to shuttle the working gas between the hot and cold heat exchangers. When the working gas is pushed to the hot end of the cylinder it expands and pushes the power piston. When it is pushed to the cold end of the cylinder it contracts and the momentum of the machine, usually enhanced by a flywheel, pushes the power piston the other way to compress the gas. Unlike the alpha type, the beta type avoids the technical problems of hot moving seals, as the power piston is not in contact with the hot gas.


title: Stirling engine

text: A gamma Stirling is simply a beta Stirling with the power piston mounted in a separate cylinder alongside the displacer piston cylinder, but still connected to the same flywheel. The gas in the two cylinders can flow freely between them and remains a single body. This configuration produces a lower compression ratio because of the volume of the connection between the two but is mechanically simpler and often used in multi-cylinder Stirling engines.


title: Stirling engine

text: Free-piston Stirling engines include those with liquid pistons and those with diaphragms as pistons. In a free-piston device, energy may be added or removed by an electrical linear alternator, pump or other coaxial device. This avoids the need for a linkage, and reduces the number of moving parts. In some designs, friction and wear are nearly eliminated by the use of non-contact gas bearings or very precise suspension through planar springs.


title: Stirling engine

text: In the early 1960s, William T. Beale of Ohio University located in Athens, Ohio, invented a free piston version of the Stirling engine to overcome the difficulty of lubricating the crank mechanism. While the invention of the basic free piston Stirling engine is generally attributed to Beale, independent inventions of similar types of engines were made by E.H. Cooke-Yarborough and C. West at the Harwell Laboratories of the UK AERE. G.M. Benson also made important early contributions and patented many novel free-piston configurations.


title: Stirling engine

text: The first known mention of a Stirling cycle machine using freely moving components is a British patent disclosure in 1876. This machine was envisaged as a refrigerator (i.e., the "reversed" Stirling cycle). The first consumer product to utilize a free piston Stirling device was a portable refrigerator manufactured by Twinbird Corporation of Japan and offered in the US by Coleman in 2004.


title: Stirling engine

text: Design of the flat double-acting Stirling engine solves the drive of a displacer with the help of the fact that areas of the hot and cold pistons of the displacer are different.


title: Stirling engine

text: The drive does so without any mechanical transmission. Using diaphragms eliminates friction and need for lubricants.


title: Stirling engine

text: When the displacer is in motion, the generator holds the working piston in the limit position, which brings the engine working cycle close to an ideal Stirling cycle.


title: Stirling engine

text: The ratio of the area of the heat exchangers to the volume of the machine increases by the implementation of a flat design.


title: Stirling engine

text: Flat design of the working cylinder approximates thermal process of the expansion and compression closer to the isothermal one.


title: Stirling engine

text: Thermoacoustic devices are very different from Stirling devices, although the individual path travelled by each working gas molecule does follow a real Stirling cycle. These devices include the thermoacoustic engine and thermoacoustic refrigerator. High-amplitude acoustic standing waves cause compression and expansion analogous to a Stirling power piston, while out-of-phase acoustic travelling waves cause displacement along a temperature gradient, analogous to a Stirling displacer piston. Thus a thermoacoustic device typically does not have a displacer, as found in a beta or gamma Stirling.


title: Stirling engine

text: NASA has considered nuclear-decay heated Stirling Engines for extended missions to the outer solar system. In 2018, NASA and the United States Department of Energy announced that they had successfully tested a new type of nuclear reactor called KRUSTY, which stands for "Kilopower Reactor Using Stirling TechnologY", and which is designed to be able to power deep space vehicles and probes as well as exoplanetary encampments.


title: Stirling engine

text: At the 2012 Cable-Tec Expo put on by the Society of Cable Telecommunications Engineers, Dean Kamen took the stage with Time Warner Cable Chief Technology Officer Mike LaJoie to announce a new initiative between his company Deka Research and the SCTE. Kamen refers to it as a Stirling engine.


title: Stirling engine

text: Very low-power engines have been built that run on a temperature difference of as little as 0.5 K. A "displacer-type Stirling engine" has one piston and one displacer. A temperature difference is required between the top and bottom of the large cylinder to run the engine. In the case of the "low-temperature-difference" (LTD) Stirling engine, the temperature difference between one's hand and the surrounding air can be enough to run the engine. The power piston in the displacer-type Stirling engine is tightly sealed and is controlled to move up and down as the gas inside expands. The displacer, on the other hand, is very loosely fitted so that air can move freely between the hot and cold sections of the engine as the piston moves up and down. The displacer moves up and down to cause most of the gas in the displacer cylinder to be either heated, or cooled.


title: Stirling engine

text: Stirling engines, especially those that run on small temperature differentials, are quite large for the amount of power that they produce (i.e., they have low specific power). This is primarily due to the heat transfer coefficient of gaseous convection, which limits the heat flux that can be attained in a typical cold heat exchanger to about 500 W/(m·K), and in a hot heat exchanger to about 500–5000 W/(m·K). Compared with internal combustion engines, this makes it more challenging for the engine designer to transfer heat into and out of the working gas. Because of the thermal efficiency the required heat transfer grows with lower temperature difference, and the heat exchanger surface (and cost) for 1 kW output grows with (1/ΔT). Therefore, the specific cost of very low temperature difference engines is very high. Increasing the temperature differential and/or pressure allows Stirling engines to produce more power, assuming the heat exchangers are designed for the increased heat load, and can deliver the convected heat flux necessary.


title: Stirling engine

text: A Stirling engine cannot start instantly; it literally needs to "warm up". This is true of all external combustion engines, but the warm up time may be longer for Stirlings than for others of this type such as steam engines. Stirling engines are best used as constant speed engines.


title: Stirling engine

text: Power output of a Stirling tends to be constant and to adjust it can sometimes require careful design and additional mechanisms. Typically, changes in output are achieved by varying the displacement of the engine (often through use of a swashplate crankshaft arrangement), or by changing the quantity of working fluid, or by altering the piston/displacer phase angle, or in some cases simply by altering the engine load. This property is less of a drawback in hybrid electric propulsion or "base load" utility generation where constant power output is actually desirable.


title: Stirling engine

text: The gas used should have a low heat capacity, so that a given amount of transferred heat leads to a large increase in pressure. Considering this issue, helium would be the best gas because of its very low heat capacity. Air is a viable working fluid, but the oxygen in a highly pressurized air engine can cause fatal accidents caused by lubricating oil explosions. Following one such accident Philips pioneered the use of other gases to avoid such risk of explosions.


title: Stirling engine

text: In most high-power Stirling engines, both the minimum pressure and mean pressure of the working fluid are above atmospheric pressure. This initial engine pressurization can be realized by a pump, or by filling the engine from a compressed gas tank, or even just by sealing the engine when the mean temperature is lower than the mean operating temperature. All of these methods increase the mass of working fluid in the thermodynamic cycle. All of the heat exchangers must be sized appropriately to supply the necessary heat transfer rates. If the heat exchangers are well designed and can supply the heat flux needed for convective heat transfer, then the engine, in a first approximation, produces power in proportion to the mean pressure, as predicted by the West number, and Beale number. In practice, the maximum pressure is also limited to the safe pressure of the pressure vessel. Like most aspects of Stirling engine design, optimization is multivariate, and often has conflicting requirements. A difficulty of pressurization is that while it improves the power, the heat required increases proportionately to the increased power. This heat transfer is made increasingly difficult with pressurization since increased pressure also demands increased thicknesses of the walls of the engine, which, in turn, increase the resistance to heat transfer.


title: Stirling engine

text: At high temperatures and pressures, the oxygen in air-pressurized crankcases, or in the working gas of hot air engines, can combine with the engine's lubricating oil and explode. At least one person has died in such an explosion. Lubricants can also clog heat exchangers, especially the regenerator. For these reasons, designers prefer non-lubricated, low-coefficient of friction materials (such as rulon or graphite), with low normal forces on the moving parts, especially for sliding seals. Some designs avoid sliding surfaces altogether by using diaphragms for sealed pistons. These are some of the factors that allow Stirling engines to have lower maintenance requirements and longer life than internal-combustion engines.


title: Stirling engine

text: Theoretical thermal efficiency equals that of the hypothetical Carnot cycle, i.e. the highest efficiency attainable by any heat engine. However, though it is useful for illustrating general principles, the ideal cycle deviates substantially from practical Stirling engines. It has been argued that its indiscriminate use in many standard books on engineering thermodynamics has done a disservice to the study of Stirling engines in general.


title: Stirling engine

text: Stirling engines cannot achieve total efficiencies typical of an internal combustion engine, the main constraint being thermal efficiency. During internal combustion, temperatures achieve around 1500 °C–1600 °C for a short period of time, resulting in greater mean heat supply temperature of the thermodynamic cycle than any Stirling engine could achieve. It is not possible to supply heat at temperatures that high by conduction, as it is done in Stirling engines because no material could conduct heat from combustion in that high temperature without huge heat losses and problems related to heat deformation of materials.


title: Stirling engine

text: Stirling engines are capable of quiet operation and can use almost any heat source. The heat energy source is generated external to the Stirling engine rather than by internal combustion as with the Otto cycle or Diesel cycle engines. This type of engine is currently generating interest as the core component of micro combined heat and power (CHP) units, in which it is more efficient and safer than a comparable steam engine. However, it has a low power-to-weight ratio, rendering it more suitable for use in static installations where space and weight are not at a premium.


title: Stirling engine

text: Other real-world issues reduce the efficiency of actual engines, due to the limits of convective heat transfer and viscous flow (friction). There are also practical, mechanical considerations: for instance, a simple kinematic linkage may be favoured over a more complex mechanism needed to replicate the idealized cycle, and limitations imposed by available materials such as non-ideal properties of the working gas, thermal conductivity, tensile strength, creep, rupture strength, and melting point. A question that often arises is whether the ideal cycle with isothermal expansion and compression is in fact the correct ideal cycle to apply to the Stirling engine. Professor C. J. Rallis has pointed out that it is very difficult to imagine any condition where the expansion and compression spaces may approach isothermal behavior and it is far more realistic to imagine these spaces as adiabatic. An ideal analysis where the expansion and compression spaces are taken to be adiabatic with isothermal heat exchangers and perfect regeneration was analyzed by Rallis and presented as a better ideal yardstick for Stirling machinery. He called this cycle the 'pseudo-Stirling cycle' or 'ideal adiabatic Stirling cycle'. An important consequence of this ideal cycle is that it does not predict Carnot efficiency. A further conclusion of this ideal cycle is that maximum efficiencies are found at lower compression ratios, a characteristic observed in real machines. In an independent work, T. Finkelstein also assumed adiabatic expansion and compression spaces in his analysis of Stirling machinery


title: Stirling engine

text: The ideal Stirling cycle is unattainable in the real world, as with any heat engine. The efficiency of Stirling machines is also linked to the environmental temperature: higher efficiency is obtained when the weather is cooler, thus making this type of engine less attractive in places with warmer climates. As with other external combustion engines, Stirling engines can use heat sources other than the combustion of fuels. For example, various designs for solar-powered Stirling engines have been developed.


title: Stirling engine

text: In contrast to internal combustion engines, Stirling engines have the potential to use renewable heat sources more easily, and to be quieter and more reliable with lower maintenance. They are preferred for applications that value these unique advantages, particularly if the cost per unit energy generated is more important than the capital cost per unit power. On this basis, Stirling engines are cost-competitive up to about 100 kW.


title: Stirling engine

text: Compared to an internal combustion engine of the same power rating, Stirling engines currently have a higher capital cost and are usually larger and heavier. Their lower maintenance requirements make the overall "energy" cost comparable. The thermal efficiency is also comparable (for small engines), ranging from 15% to 30%. For applications such as micro-CHP, a Stirling engine is often preferable to an internal combustion engine. Other applications include water pumping, astronautics, and electrical generation from plentiful energy sources that are incompatible with the internal combustion engine, such as solar energy, and biomass such as agricultural waste and other waste such as domestic refuse. However, Stirling engines are generally not price-competitive as an automobile engine, because of high cost per unit power, & low power density.


title: Stirling engine

text: Applications of the Stirling engine range from heating and cooling to underwater power systems. A Stirling engine can function in reverse as a heat pump for heating or cooling. Other uses include combined heat and power, solar power generation, Stirling cryocoolers, heat pump, marine engines, low power model aircraft engines, and low temperature difference engines.


title: Gewehr 98

text: The Gewehr 98 (abbreviated G98, Gew 98, or M98) is a German bolt-action rifle made by Mauser, firing cartridges from a five-round internal clip-loaded magazine. It was the German service rifle from 1898 to 1935, when it was replaced by the Karabiner 98k, a shorter weapon using the same basic design. The Gewehr 98 action, using a stripper clip loaded with the 7.92×57mm Mauser cartridge, successfully combined and improved several bolt-action engineering concepts which were soon adopted by many other countries, including the United Kingdom, United States, and Japan. The Gewehr 98 replaced the earlier Gewehr 1888 as the main German service rifle. It first saw combat in the Chinese Boxer Rebellion and was the main German infantry service rifle of World War I. The Gewehr 98 saw further military use by the Ottoman Empire and Nationalist Spain.


title: Gewehr 98

text: The Gewehr 98 was introduced into German military service in 1898, replacing the Gewehr 1888. The bolt-action design was the latest refinement of the 1895 design patented by Paul Mauser on 9 September 1895. Mauser was already selling similar 1895-design weapons to many other countries, and had supplied less advanced Mauser rifles to the German Army from 1871 to 1888. The 1888 replacement for the Mauser was an internal design from the army, but failed through an impractical design. In the interim decade, Mauser rifles became recognized as the world standard, and the German Army became outclassed by a German-made product in the hands of others.


title: Gewehr 98

text: The German "Gewehr-Prüfungskommission" ("G.P.K.") (rifle testing commission) adopted the Gewehr 98 on 5 April 1898. The action was derived from the experimental Gewehr 96 rifle. In 1901, the first troop issues of the Gewehr 98 rifles were made to the East Asian Expeditionary Force, the Imperial German Navy, and three premier Prussian army corps. The first combat use of the Gewehr 98 was during the Boxer Rebellion (1898–1901). In 1904, contracts were placed with Waffenfabrik Mauser for 290,000 rifles and Deutsche Waffen und Munitionsfabriken (DWM) for 210,000 rifles. At the outbreak of WWI in 1914, the German Army had 2,273,080 Mauser 98-rifles of all types; an additional 7,000,000 were produced during the war.


title: Gewehr 98

text: The 8 mm M/88 cartridge which was introduced in 1888 and loaded with an 8.08 mm (.318 in) 14.6 g (226 gr) round nose bullet was replaced on 3 April 1903, by the 7.92×57mm Mauser "S Patrone" (S ball cartridge) which was loaded with a new 8.20 mm (.323 in) 9.9 g (154 gr) spitzer bullet. The ammunition conversion was indicated by a small "S" stamped above the chamber and on the barrel at the back of the rear sight base. This was done since the 1888 pattern M/88 cartridge and 1903 S-bore pattern cartridge are two different non-interchangeable chamberings. Since the new IS cartridge had a flatter trajectory the "Lange Visier" rear sight had to be changed with an "S"-adapted "Lange Visier".


title: Gewehr 98

text: The Gewehr 98 or model 98 (M98) rifle is a manually operated, magazine fed, controlled-feed bolt-action rifle, in length and in weight. It has a long rifled barrel and carries 5 rounds of ammunition in an internal magazine. The Gewehr 98 has two sling swivels, open front sights, and a curved tangent-type rear sight, known as the "Lange Visier".


title: Gewehr 98

text: The controlled-feed bolt-action of the Gewehr 98 is a distinct feature and is regarded as one of the major bolt-action system designs.


title: Gewehr 98

text: The controlled-feed Mauser M98 bolt-action system is based on previous 19th-century Mauser bolt-action rifle designs and is a simple, strong, safe, and well-thought-out design intended to negate as many failure modes as possible and which inspired other military and hunting/sporting rifle designs that became available during the 20th century. A drawback of the M98 system is that it cannot be cheaply mass-produced very easily. Some other bolt-action designs (e.g. the Lee–Enfield and Pattern 1914 Enfield/M1917 Enfield) offer trained operators a faster rate of fire as the ergonomic relation between the bolt handle and trigger is more favorable and they can be cycled without loss of sight picture.


title: Gewehr 98

text: The M98 system consists of a receiver that serves as the system's shroud and a bolt group of which the bolt body has three locking lugs, two large main lugs at the bolt head and a third safety lug at the rear of the bolt, which serves as a backup in case the primary locking lugs failed. This third lug is a distinctive feature and was not present on previous Mauser bolt-action designs. The two main locking lugs are positioned opposed to each other and display a locking surface of , whilst the third safety lug normally plays no part in locking the action to avoid asymmetric and hence unbalanced bolt thrust forces. The diameter of the M98 system receiver ring was also enlarged to diameter compared to previous Mauser "small ring" bolt-action designs that had diameter receiver rings for additional strength and safety. Accordingly, the barrel shank was enlarged to diameter with of threaded area at 12 threads per inch compared to previous Mauser "small shank" bolt-action designs that had diameter with of threaded area at 12 threads per inch barrel shanks for additional strength. The bolt handle is permanently attached to the bolt and, on the Gewehr 98, is straight and protrudes out for optimal leverage.


title: Gewehr 98

text: Another distinctive feature of the M98 system is the controlled-feed mechanism, consisting of a large, non-rotating claw extractor that engages the cartridge case rim as soon as the round leaves the magazine and firmly holds the cartridge case until the round is ejected by the ejector, mounted inside the receiver. Combined with a slight bolt retraction at the last stage of the bolt opening cycle, caused by the cammed surface on the rear receiver bridge, this results in a positive cartridge case extraction. The M98 bolt-action will cycle correctly, irrespective of the way the rifle is moved or positioned during the bolt cycling action or if the cartridge has been fired or not. Only if the bolt is not brought back far enough, sharply enough, in a controlled round feed bolt-action the cartridge case may not be cleanly ejected and a jam may result.


title: Gewehr 98

text: The bolt houses the firing pin mechanism that cocks when the bolt is opened, and the cocking piece protrudes visually and tactilely from the rear of the bolt to indicate the action is cocked. A cocking shroud lock that was not present on previous Mauser bolt-action designs was added. The distance the firing pin needs to travel was decreased to reduce and hence improve lock time – the amount of time between initiating the firing sequence by releasing the trigger and the firing pin striking the primer that ignites the propellant contained in the 7.92×57mm Mauser cartridge.


title: Gewehr 98

text: The M98 action features two large oval shaped gas relief holes on the bottom of the bolt, which when catastrophic failures like a primer, cartridge rupture or detonation occur relieve high pressure gases into the magazine, and a gas shield on the bolt sleeve. Military M98 systems feature a secondary gas relief where gas is routed down the locking lug raceway to a thumb hole cutout exit on left side of receiver. Civilian M98 systems often lack the thumb hole cut out, as the ammunition feeding is generally simplified to single round feeding only. These safety features are designed to route escaping gas out of the bolt and eventual debris away from the operator's face.


title: Gewehr 98

text: The M98 bolt group can be easily removed from the receiver simply by rotating the safety lever to the 12 o'clock position and pulling out the bolt stop lever, located at the rear left wall of the receiver, and then operate the action and continue rearward bolt travel past the bolt stop. The metal disc inlay in the stock functions as a bolt disassembly tool.


title: Gewehr 98

text: Many metal parts of the Gewehr 98 were blued, a process in which steel is partially protected against rust by a layer of magnetite (FeO). Such a thin black oxide layer provides minimal protection against rust or corrosion, unless also treated with a water-displacing oil to reduce wetting and galvanic corrosion. From 1905 until 1945 the German military used Ballistol intended for cleaning, lubricating, and protecting metallic, wooden and leather firearms parts.


title: Gewehr 98

text: A three-position safety attached at the rear of the bolt which operating lever can be flicked from right (safety on, bolt locked) to middle (safety on, bolt can be opened for reloading), to left (ready to fire), but only when the rifle is cocked; otherwise, the safety will not move. The safety secures the firing pin. The safety catch lever is quite large, making it easy to operate, but posing a problem for mounting telescopic sights low above the receiver whilst retaining good operability of the safety catch lever.


title: Gewehr 98

text: The internal magazine of the M98 system consists of an integral box machined to match the cartridge for which the rifle was being chambered, with a detachable floorplate, that can hold up to 5 rifle cartridges. The German military M98 system internal magazine boxes feature an internal magazine length of to store maximal overall length 7.92×57mm Mauser cartridges without dimensional issues. The cartridges are stored in the magazine box in a staggered column at a stacking angle of 30 degrees, so viewed from the end, three cartridges touching each other form the points of an equilateral triangle. The magazine can be loaded with single rounds by pushing the cartridges into the receiver top opening or via stripper clips. Each stripper clip can hold 5 rounds to fill the magazine and is inserted into clip guides machined into the rear receiver bridge. After loading, the empty clip is ejected when the bolt is closed. For easier loading a crescent shaped thumb hole cutout is present at the left rear of the receiver top. The magazine can be unloaded by operating the bolt (the safety should, for safety reasons, be set to the middle position for this) or, in case of mechanical problems, by opening the magazine floorplate, which is flush with the stock, with the help of a cartridge tip.


title: Gewehr 98

text: Alternatively cartridges can be loaded singly directly into the chamber, as is standard on military rifles of the period, since the extractor is spring-loaded and designed so the extractor claw "pops" over the rim of the cartridge on closing.


title: Gewehr 98

text: The Gewehr 98 had no magazine cut-off mechanism, which when engaged permits the feeding and extraction of single cartridges only while keeping the cartridges in the magazine in reserve. Like the M98 system Mauser magazine fed bolt-action systems were generally not manufactured with magazine cut-offs, the Ottoman Mauser Model 1893 variant being the exception.


title: Gewehr 98

text: Though the production of the M98 system for the German military ceased at the end of World War II in 1945, the production of new Mauser M 98 and Mauser M 98 Magnum rifles for civil users has been resumed in 1999 by "Mauser Jagdwaffen GmbH" (Mauser Hunting Weapons Ltd.), according to original drawings of 1936 and the respective Mauser patents. These rifles retail (2009) for approximately EUR 6,800 for the basic Mauser M 98 version, but the addition of (luxury) options can make these rifles much more expensive. Several other gun manufacturers and custom gun builders also currently produce new M98 system clones or M98 inspired bolt-action hunting/sporting rifles. Desirable features of the M98 system, like its controlled feeding, were carried over to a host of later bolt-action designs. These designs feature technical alterations to simplify production and technical and ergonomic improvements.


title: Gewehr 98

text: The rifle had a two-stage trigger with considerable take up before the trigger engages the sear. This feature aids in preventing premature firing during stressful (combat) situations.


title: Gewehr 98

text: Originally the Gewehr 98 sight line had an open post type front sight, and a curved tangent-type rear sight with a V-shaped rear notch, known as the "Lange Visier" (Lange sight after its designer Lieutenant Colonel Lange). The rear sight was graduated for 1888 pattern M/88 cartridges from to in increments. The M/88 cartridge was loaded with full metal jacket projectiles of the round-nosed type.


title: Gewehr 98

text: The standard open iron sight aiming elements consisted of relatively coarse rugged aiming elements making the sightline suitable for rough handling and low light usage, but less suitable for aiming at small point targets. The tracks of the rear sight obstructed the view to the sides during aiming. The sights were designed with distant area fire targets like charging horseman units in mind, so the standard iron sight line could be calibrated for very long ranges. Military doctrine in the late 19th and early 20th centuries considered firing at distant area targets, where an officer would call out the range and the soldiers shot in volley, normal.


title: Gewehr 98

text: German government driven efforts to improve the performance of the military M/88 ammunition and the service arms in which the M/88 was used resulted in the design by the "Gewehr-Prüfungskommission" and adaptation in 1903 of the dimensionally redesigned 7.92×57mm Mauser chambering. Besides the chambering, the bore (designated as "S-bore") was also dimensionally redesigned. The 1903 pattern 7.92×57mm Mauser "S Patrone" (S ball cartridge) was loaded with a lighter , pointed "Spitzgeschoß" (spitzer bullet) of diameter and more powerful double-base (based on nitrocellulose and nitroglycerin) smokeless powder. With the improved ballistic coefficient of the new spitzer bullet, the 1903 pattern cartridge had an improved maximum effective range and a flatter trajectory, and was therefore less critical of range estimation compared to the M/88 cartridge. With the introduction of the "S Patrone" the rear sight graduation was changed accordingly and could be regulated from to in increments.


title: Gewehr 98

text: While the modified sight line for 1903 pattern 7.92×57mm Mauser "S Patrone" IS cartridges was calibrated for a minimum zero distance of and can result in hitting high when using the open post front sight and V-shaped rear notch at close range, the pillars formed by the tracks of the rear sight allow closer targets to be quickly bracketed between the "goalposts", a sighting method that automatically compensates for the high point of aim using the normal sighting method at sub- ranges.


title: Gewehr 98

text: The Gewehr 98 oil finished rifle stock features a semi-pistol grip. A top handguard was standard on all rifles and extended from the front of the rear sight base terminating just ahead of the bottom barrel band. A steel cross bolt was mounted to distribute the forces and hence the effects of recoil on the stock bedding, reducing the chance to split the stock. The stock featured a quick detachable sling swivel on the underside of the butt stock, a top swivel located underneath the bottom barrel band, and a parade hook mounted on the underside of the top H-style barrel band. The prewar stocks were produced from walnut wood and were aged for an average of three years to allow the wood to stabilize. Beginning in 1917, walnut shortages necessitated the use of beech wood. The late-war production beech stocks were less durable and heavier than the original walnut stocks.


title: Gewehr 98

text: The rifle was issued with a leather carrying sling. During the duration of World War I, due to a shortage of leather, slings were produced out of canvas.


title: Gewehr 98

text: The rifle was able to fire rifle grenades. Various attachable rifle grenade launcher models were designed during World War I.


title: Gewehr 98

text: The Gewehr 98 was designed to be used with a bayonet. For this the rifle had a H-style top barrel-band with a long bayonet lug. The long bearing surface on the Gewehr 98 bayonet lug eliminated the addition of a muzzle ring. The advantage of this solution lies in the fact that muzzle rings can interfere with barrel oscillation which can significantly impede the accuracy of a rifle. The rifle was originally issued with the "Seitengewehr 98" pattern bayonet. This épée style bayonet has a long quillback blade. By the end of 1905, this bayonet began to be replaced with the more robust and practical "Seitengewehr 98/05", with a blade. It was called the "Butcher Blade" by the Allies due to its distinctive shape, and was initially intended for artillerymen and engineers as a chopping tool as well as a weapon. Towards the end of World War I, the blade "Seitengewehr 84/98" was introduced as an economy measure and because the longer models were impractical in narrow trenches; this model became standard issue during the Weimar Republic and Third Reich. Serrated, saw-backed versions of the standard patterns intended to be used as tools were carried by German "Pioniere" (pioneers).


title: Gewehr 98

text: In the spring of 1915, it was decided to fit 15,000 Gewehr 98 rifles, selected for being exceptionally accurate during factory tests, with telescopic sights for sniper use, though the Gewehr 98 was not designed for use with aiming optics. The "Scharfschützen-Gewehr 98" (sniper rifle 98) was officially adapted in 1915 featuring for the period advanced 4× Görtz or Zeiss telescopic sights. These sights were mounted offset to the left to allow stripper clip loading of the rifle and the sights had a bullet drop compensation sight drum out to 1,000 m range in 100 m increments. The bolt handle had to be turned-down from its original straight design. In the stock, a recess had to be made to accommodate the turned-down bolt handle modification.


title: Gewehr 98

text: The wartime "Scharfschützen-Gewehr 98" program intended to regularize equipment issued for snipers but failed. The telescopic sights used consisted of 2.5×, 3× and 4× models, made by manufactures like Görtz, Gérard, Oigee, Zeiss, Hensoldt, Voigtländer and various civilian models from manufacturers like Bock, Busch and Füss. Several different mountings produced by various manufacturers were used. Even with a turned-down bolt handle (unless it is low-profile as is common practice with modern hunting rifles), optics mounted low directly above the receiver will not leave enough space between the rifle and the telescopic sight body for unimpaired operation of the bolt or three-position safety catch lever. This ergonomic problem was solved by mounting the telescopic sight relatively high above the receiver. By the end of World War I, 18,421 Gewehr 98 rifles were converted and equipped with telescopic sights and issued to German snipers.


title: Gewehr 98

text: Not to be confused with the later Karabiner 98k or the earlier Karabiner 98A (uppercase A), the Karabiner 98a (Kar 98a) was a shorter version of the Gewehr 98 originally made for cavalry and support unit use. The Karabiner 98A, adopted in February 1902, had a considerably shorter barrel than the Gewehr 98 and was also lighter at empty. Experiments in 1904 with Karabiner 98A carbines rechambered for the "S Patrone" cartridge showed excessive recoil and muzzle flash problems, leading to the suspension of production in 1905.


title: Gewehr 98

text: The "Gewehr Prüfungs Kommission" (GPK) started developing a new carbine with a longer barrel and a different stock to address these problems; by the mid-summer of 1907, the longer barrelled prototype carbines showed more acceptable recoil and muzzle blast behavior with the "S Patrone".


title: Gewehr 98

text: In January 1908, the Karabiner Model 1898 AZ (Kar 98AZ) was accepted for service. The new features were a small diameter () receiver ring, tapered rather than stepped barrel contour, an L-shaped stacking rod attached to the stock near the muzzle, and a turned-down bolt handle and recess in the stock in the same fashion as the Gewehr 98s sniper variant. The "AZ" stands for "Aufpflanz-und-Zusammensetzvorrichtung", meaning "with bayonet attachment point and stacking rod". At the end of World War I about 1,500,000 short rifles had been produced. In 1923, the AZ was renamed to 'a', as Germany sought to distinguish the model from the newer 'b' and 'k' models.


title: Gewehr 98

text: During World War I, the Karabiner 98a was issued to light infantry, cavalry, mountain troops, and later to assault troops. It was liked because it was lighter and shorter than the Gewehr 98, and was thus better suited for use in trench assaults.


title: Gewehr 98

text: The Karabiner 98b was not technically another "carbine" variant, but rather was a rifle designated as a carbine to comply with the terms of the Treaty of Versailles which only allowed Germany to produce carbines. The Karabiner Model 1898b was introduced in 1923. The Karabiner 98b had a tangent rear sight as opposed to the original "Lange" ramp sight, a wider lower band with side sling attachment bar, a side butt attachment point for a sling, and a turned down bolt handle. It was otherwise merely a modified form of the Gewehr 98, from which the Karabiner 98k was derived.


title: Gewehr 98

text: The Gewehr 98 saw service primarily in World War I, as well as the Boxer Rebellion and the Herero Wars in the preceding years. As with all contemporary bolt-action rifles, it was a powerful and accurate rifle with long range that was poorly suited for the close quarter fighting of trench warfare. The considerable length of the rifle and the minimum sight setting of 400 meters (far in excess of the typical range in trench battles) were particular handicaps.


title: Gewehr 98

text: Its successor, the Karabiner 98k, would go on to be the standard rifle of the German infantry during World War II. Some Gewehr 98s also saw service in World War II, though many of these older rifles were converted to either 98b or 98k specifications.


title: Gewehr 98

text: For determining accuracy the German military fired a group of shots into a target and used statistics to calculate a hit probability. For this they drew a circle that disregards the hits on the outer part of the target and only count half of the hits (50% or R) on the inner part of the circle. They then used both the vertical and horizontal measurements of the reduced shotgroup to measure accuracy. When the R results are doubled the hit probability increases to 93.7%.


title: Gewehr 98

text: These requirements were carried over for the Karabiner 98k, Germany's standard service rifle during WW2, each rifle having to place 5 out of 5 shots within a 12cm circle at 100 m in order to be accepted for service.


title: Gewehr 98

text: For reference a 1 minute of arc (MOA) circle at has a diameter of , at equals 2.06 MOA, and at equals 4.12 MOA.


title: Gewehr 98

text: The circular error probable method employed by the Germans and other European militaries cannot be converted and is not comparable to the common US methods (groupsize of 5 or 10 successive shots fired at 100 yards) for determining accuracy and the British method of four out of five successive shots fired at 100 feet must hit a rectangle measuring 1 inch wide × 1.5 inches high


title: Gewehr 98

text: According to pre World War I military instructions booklets new Gewehr 98 rifles firing "S Patrone" ball ammunition on average had (3.9 MOA) vertical dispersion and (3.2 MOA) horizontal dispersion at . New Karabiner 98AZ / Karabiner 98a (small receiver ring, shorter version of the Gewehr 98) firing "S Patrone" ball ammunition on average had (4.9 MOA) vertical dispersion and (3.9 MOA) horizontal dispersion at . Individual weapons can shoot better or worse than these averages.


title: Gewehr 98

text: For comparison the acceptance accuracy requirements for various US service rifles at as well as the British Lee Enfield No.4 Mk.I rifle at .


title: Gewehr 98

text: The accuracy standards of the Gewehr 98 and most other service rifles used in World War I were similar.


title: Gewehr 98

text: The Mauser M 98 was a civilian version adapted for hunting and other sporting purposes of the Gewehr 98 service rifle. Vaguely similar to the latter rifle in appearance, the M 98 was offered in many different hunting chamberings, not like the original service rifle. The Mauser M 98 series offered several features and factory options, that are also typical for sporterised ex-service rifles, ranging from various technical departures from the basic Mauser service rifle it was based on to luxury wood grades, (gold) inlays, engravings and surface treatments like color case hardening. Some of the available options were originally developed and introduced by John Rigby & Co. on Rigby Mauser hunting rifles.


title: Gewehr 98

text: John Rigby & Co. commissioned Mauser to develop the M 98 magnum action in the early 1900s. It was designed to function with the large sized cartridges normally used to hunt Big Five game and other dangerous game species. For this specialized type of hunting, where absolute reliability of the rifle under adverse conditions is very important, the controlled-feed M 98 system remains the standard by which other action designs are judged. In 1911 John Rigby & Co. introduced the .416 Rigby cartridge that due to its dimensions could only be used in the M 98 magnum action.


title: Gewehr 98

text: After World War I, the Treaty of Versailles left Germany extremely constricted in terms of military power. Civilians were not allowed to have any use of standard military weapons or ammunition. Since the 7.92×57mm Mauser round was so stout and great for hunting, people did not want to give up on it, so a redesign of the cartridge was made for the civilian market resulting in the 8×60mm S featuring a new longer case. The 8×60mm S cartridge was kept under overall length to fit the cartridge in standard military M98 magazine boxes without any modification.


title: Gewehr 98

text: The also rare 8×64mm S cartridge offers a comparable rechambering option for Mauser Gewehr 98 and Karabiner 98k rifles sporting 8mm S-bores. Due to its larger case capacity the 8×64mm S chambering offers better ballistic performance than the 8×60mm S. Some custom rifles were made using Mauser 98's and rechambering them for the 9×57mm Mauser.


title: Gewehr 98

text: Since the purpose for these rifles was hunting and sporting, the bolt handle was professionally bent down, gradually the bent bolt handle became the standard and replaced the older straight style (though that was of course not always the case). The standard military sights were replaced by a 100 m sight, along with a flip-up on the rear sight for 200 m. The military stocks were replaced by newer ones that did not include the extra length of stock needed for the bayonet lug.


title: Gewehr 98

text: Today these sporter rifles are extremely rare and the 8×60mm S, 8×64mm S and 9×57mm Mauser cartridges are nearly obsolete, as only few mainstream ammunition manufacturers along with some other smaller companies continue to produce them. When correct ammunition is used in a converted rifle, an 8×60mm S, 8×64mm S or 9×57mm Mauser modified Gewehr 98 can be an extremely potent and inexpensive long-range big-game rifle.


title: Gewehr 98

text: Also, many Gewehr 98 rifles acquired as trophies by Allied forces during the war and brought to the US were converted to the 8mm-06 wildcat cartridge, a modification of the original 8×57mm IS chambering to 8×63mm S to accommodate the use of the plentiful .30-06 Springfield brass for reloading, with 8mm (.323 caliber) bullets. Such conversions are indistinguishable from unmodified rifle without careful examination, and can be quite dangerous if fired with the shorter 8×57mm ammunition, as the cartridge case will stretch to fit the elongated chamber and possibly rupture in the process, which causes a potentially highly dangerous high pressure propellant gas leakage. However, the Mauser M 98 action is designed specifically to direct gas away from the shooter in the event of a case rupture.


title: Gewehr 98

text: In the 21st century the US based company Rhineland Arms started to produce .45 ACP conversion kits for the Mauser action using M1911 pistol magazines.


title: Gewehr 98

text: Many were converted to shotguns, typically in 12 and 16-gauge, as well as a few in 20-gauge. In making the conversion, both main locking lugs were typically removed. The magazine was altered to allow a single shell in reserve. Many authorities recommend against firing these guns, particularly with modern magnum shotshells.


title: Gewehr 98

text: The Weimar Republic, the successor state to the German Empire, implemented a program designed to update their remaining supplies of Gewehr 98 rifles for the Reichswehr in the years following World War I. Rifles allowed into service with the early Weimar security forces were stamped with a "1920" marking on their receiver ring. Further updates to Weimar-era Gewehr 98's often included the replacement of the Lange Visier rear sight with a standard Karabiner 98k-style rear sight. Many of the Gew 98 were also converted to the Kar 98b configuration, with a turned bolt handle, new tangent leaf sight and a hole cut through the side of the stock to accommodate a Karabiner 98k-style side-mounted sling system, but some Karabiner 98b were also produced from new parts. Some of these rifles saw use in World War II but mostly in second line units because the shortened and improved Karabiner 98k was the standard issue rifle by that time. Gewehr 98 and Karabiner 98b were sometimes rebuilt to the Karabiner 98k configuration. In 1924 the Gewehr 98 was developed into the Mauser Standardmodell rifle.


title: Gewehr 98

text: During World War II the Germans captured German-made Yugoslav Model 1898 carbines and rifles and designated them "Gewehr 298 (j)" and "Karabiner 492 (j)". The "Volkssturm" ("People's Militia") also made use of the Gewehr 98 and Kar 98a; out of all their mixed arsenal the Gewehr 98 was probably the best since it used standard 7.92×57mm IS rounds and a man trained on a Karabiner 98k could transition over to the Gewehr 98 easily since the actions of both rifles were the same.


title: Gewehr 98

text: After 1945, some ex-German Karabiner 98b were also taken into French Army service, the only modification being the use of the sling of the MAS-36 rifle.


title: Gewehr 98

text: The Ottoman Empire bought the Mauser Model 1903. The Mauser 1903 was a modified version Gewehr 98. The Lange Visier sight was replaced by a tangent leaf sight, the nose cap was simplified, the rifle could be fitted with older Ottoman M1890 bayonets. The weapon had curved arm on its bolt stop to block the cartridge clip when the cartridges are stripped into the magazine. It also had a larger receiver and a longer cocking cam and firing pin than the German variant. After the adoption of the long rifle, 200,000 were received before 1905. 406 Marine-gewehre were delivered to the Ottoman Navy in 1904, 7,617 to the Gendarmerie in Ottoman Macedonia. 1,100 more, modified to fire spitzer bullets and sometimes known as M1910, were ordered in 1910. The Ottoman customs also received some. The Model 1905 carbine was produced between 1903 and 1906. 30,000 M1908 carbines were delivered in 1908 and 1909.


title: Gewehr 98

text: The Model 1903 saw combat during the Italo-Turkish War, the Balkan Wars, World War I and the Turkish War of Independence. After World War I, most of these weapons were modified to fire the 7.92×57mm Mauser round. Many of the long rifles were refurbished as Mauser Model 1938 short rifles. Models 1903 and 1905 were still in service in the 1960s, large numbers of Gewehr 98 rifles were also given to the Ottoman Empire both during and after World War I, including the majority of 1916 Waffenfabrik Oberndorf production. Many of these rifles were converted to the "M38" standard by the Republic of Turkey in the years before, during, and after World War I. Today these rifles are widely available in North America along with other Turkish Mausers. Careful observation is usually needed to tell an Ex-Gewehr 98 apart from the myriad of other common M38-standard Mausers.


title: Gewehr 98

text: After Czechoslovakia was founded in 1918, they bought 57 000 Gewehr 98 rifles from Netherlands (the so-called Netherlands block), which was acquired from disarmed German troops on Netherlands territory. After examination of Gewehr 98 Czechoslovakia developed own improved version known as Puška vz. 24 (Rifle mod. 24). That rifle, produced from 1924 to 1942, became the standard weapon of Czechoslovak forces before WWII and up to the 1960s. It was also commercially successful - among users were Romania, China, Bolivia, Turkey, Japan, Spain, Iran (also locally produced under licence), Ecuador, Brasil, Lithuania, Yugoslavia; after WWII also Israel, North Vietnam and many others).


title: Gewehr 98

text: The rifle saw some usage in the Spanish Civil War, mostly in the hands of Generalissimo Franco's Nationalists and German volunteer legions. Most of these rifles were bought and exported to the United States as cheap sporting rifles in the 1960s by Interarmco.


title: Gewehr 98

text: After the Second Polish Republic got its independence from the German Empire the Polish government got control over the state arsenal in former Danzig. The tools and machine park was moved to Warsaw to set up a state arsenal to equip the new Polish army. The machine park was set up to produce German G98 rifles and Kar98AZ carbines. A nearly unchanged version of the G98 was produced an accepted by the Polish army as "Karabin wz.1898" abbreviated and marked "G98" or "W98" for infantry use. In 1921 a Polish version of the German Kar98AZ was produced for the cavalry accepted as "Karabinek wz. 1898" abbreviated and marked "K98" a remarkable difference is the strengthen staking hook. Problems with this carbine surfaced including intense muzzle blast and flash. In 1939 the K98 was phased out in favor to the K29 a Polish version of the Czech vz. 24 this carbine was not satisfactory either. This led to the development of the K98a.


title: Gewehr 98

text: During the formation of the state of Israel in the aftermath of World War II, the Haganah acquired substantial numbers of Karabiner 98k rifles from any European sources they could find. Some of these rifles were converted Gewehr 98 rifles, which aside from the Imperial German markings are identical to all other Israeli Mausers. Like other Israeli Mausers, most of these rifles were rebarreled for 7.62×51mm NATO after that round was adopted as the Israeli standard in 1958.


title: Gewehr 98

text: Many non-German military service rifles and carbines were derived from and/or based on the Mauser M98 bolt-action system. Some of these were German-made by various contractors other than Mauser:


title: Gewehr 98

text: Following the collapse of the German Empire after World War I, many countries that were using Mauser models chose to develop, assemble, or modify their own rifle designs that were derived from and/or based on the Mauser M98 bolt-action:


title: Gewehr 98

text: The Winchester Model 54 and later the popular Winchester Model 70 are both based on the Mauser style action.


title: Gewehr 98

text: After World War II the Mauser M98 bolt-action system was used by Yugoslavia to design the Zastava M48 and Spain to design the FR8.


title: Croatian language

text: Croatian (; "" ) is the standardized variety of the Serbo-Croatian pluricentric language used by Croats, principally in Croatia, Bosnia and Herzegovina, the Serbian province of Vojvodina, and other neighboring countries. It is the official and literary standard of Croatia and one of the official languages of the European Union. Croatian is also one of the official languages of Bosnia and Herzegovina and a recognized minority language in Serbia and neighboring countries.


title: Croatian language

text: Standard Croatian is based on the most widespread dialect of Serbo-Croatian, Shtokavian, more specifically on Eastern Herzegovinian, which is also the basis of Standard Serbian, Bosnian, and Montenegrin. In the mid-18th century, the first attempts to provide a Croatian literary standard began on the basis of the Neo-Shtokavian dialect that served as a supraregional "lingua franca" pushing back regional Chakavian, Kajkavian, and Shtokavian vernaculars. The decisive role was played by Croatian Vukovians, who cemented the usage of Ijekavian Neo-Shtokavian as the literary standard in the late 19th and the beginning of the 20th century, in addition to designing a phonological orthography. Croatian is written in Gaj's Latin alphabet.


title: Croatian language

text: Besides the Shtokavian dialect, on which Standard Croatian is based, there are two other main dialects spoken on the territory of Croatia, Chakavian and Kajkavian. These dialects, and the four national standards, are usually subsumed under the term "Serbo-Croatian" in English, though this term is controversial for native speakers, and paraphrases such as "Bosnian-Croatian-Montenegrin-Serbian" are therefore sometimes used instead, especially in diplomatic circles.


title: Croatian language

text: In the late medieval period up to the 17th century, the majority of semi-autonomous Croatia was ruled by two domestic dynasties of princes ("banovi"), the Zrinski and the Frankopan, which were linked by inter-marriage. Toward the 17th century, both of them attempted to unify Croatia both culturally and linguistically, writing in a mixture of all three principal dialects (Chakavian, Kajkavian and Shtokavian), and calling it "Croatian", "Dalmatian", or "Slavonian". Historically, several other names were used as synonyms for Croatian, in addition to Dalmatian and Slavonian, and these were Illyrian (ilirski) and Slavic (slovinski). It is still used now in parts of Istria, which became a crossroads of various mixtures of Chakavian with Ekavian, Ijekavian and Ikavian isoglosses.


title: Croatian language

text: The most standardized form (Kajkavian–Ikavian) became the cultivated language of administration and intellectuals from the Istrian peninsula along the Croatian coast, across central Croatia up into the northern valleys of the Drava and the Mura. The cultural apex of this 17th century idiom is represented by the editions of ""Adrianskoga mora sirena"" ("The Siren of the Adriatic Sea") by Petar Zrinski and ""Putni tovaruš"" ("Traveling escort") by Katarina Zrinska.


title: Croatian language

text: However, this first linguistic renaissance in Croatia was halted by the political execution of Petar Zrinski and Fran Krsto Frankopan by the Holy Roman Emperor Leopold I in Vienna in 1671. Subsequently, the Croatian elite in the 18th century gradually abandoned this combined Croatian standard.


title: Croatian language

text: The Illyrian movement was a 19th-century pan-South Slavic political and cultural movement in Croatia that had the goal to standardize the regionally differentiated and orthographically inconsistent literary languages in Croatia, and finally merge them into a common South Slavic literary language. Specifically, three major groups of dialects were spoken on Croatian territory, and there had been several literary languages over four centuries. The leader of the Illyrian movement Ljudevit Gaj standardized the Latin alphabet in 1830–1850 and worked to bring about a standardized orthography. Although based in Kajkavian-speaking Zagreb, Gaj supported using the more populous Neo-Shtokavian – a version of Shtokavian that eventually became the predominant dialectal basis of both Croatian and Serbian literary language from the 19th century on. Supported by various South Slavic proponents, Neo-Shtokavian was adopted after an Austrian initiative at the Vienna Literary Agreement of 1850, laying the foundation for the unified Serbo-Croatian literary language. The uniform Neo-Shtokavian then became common in the Croatian elite.


title: Croatian language

text: In the 1860s, the Zagreb Philological School dominated the Croatian cultural life, drawing upon linguistic and ideological conceptions advocated by the members of the Illyrian movement. While it was dominant over the rival Rijeka Philological School and Zadar Philological Schools, its influence waned with the rise of the Croatian Vukovians (at the end of the 19th century).


title: Croatian language

text: Croatian is commonly characterized by the "Ijekavian" pronunciation (see an explanation of yat reflexes), the sole use of the Latin alphabet, and a number of lexical differences in common words that set it apart from standard Serbian. Some differences are absolute, while some appear mainly in the frequency of use. However, "an examination of all the major 'levels' of language shows that BCS is clearly a single language with a single grammatical system."


title: Croatian language

text: Croatian, although technically a form of Serbo-Croatian, is sometimes considered a distinct language by itself. Purely linguistic considerations of languages based on mutual intelligibility ("abstand and ausbau languages") are frequently incompatible with political conceptions of language so that varieties that are mutually intelligible can not be considered separate languages. "There is no doubt of the near 100% mutual intelligibility of (standard) Croatian and (standard) Serbian, as is obvious from the ability of all groups to enjoy each others’ films, TV and sports broadcasts, newspapers, rock lyrics etc." Differences between various standard forms of Serbo-Croatian are often exaggerated for political reasons. Most Croatian linguists regard Croatian as a separate language that is considered key to national identity. The issue is sensitive in Croatia as the notion of a separate language being the most important characteristic of a nation is widely accepted, stemming from the 19th-century history of Europe. The 1967 Declaration on the Status and Name of the Croatian Literary Language, in which a group of Croatian authors and linguists demanded greater autonomy for Croatian, is viewed in Croatia as a linguistic policy milestone that was also a general milestone in national politics. At the 50th anniversary of the Declaration, at the beginning of 2017, a two-day meeting of experts from Croatia, Bosnia-Herzegovina, Serbia and Montenegro was organized in Zagreb, at which the text of the Declaration on the Common Language of Croats, Bosniaks, Serbs and Montenegrins was drafted. The new Declaration has received more than ten thousand signatures. It states that in Croatia, Serbia, Bosnia-Herzegovina and Montenegro a common polycentric standard language is used, consisting of several standard varieties, similar to the existing varieties of German, English or Spanish. The aim of the new Declaration is to stimulate discussion on language without the nationalistic baggage and to counter nationalistic divisions.


title: Croatian language

text: The terms "Serbo-Croatian" or "Serbo-Croat" are still used as a cover term for all these forms by foreign scholars, even though the speakers themselves largely do not use it. Within ex-Yugoslavia, the term has largely been replaced by the ethnic terms Serbian, Croatian, and Bosnian.


title: Croatian language

text: The use of the name "Croatian" for a language names has been historically attested to, though not always distinctively; the Croatian–Hungarian Agreement, for example, designated "Croatian" as one of its official languages, and Croatian became an official EU language upon accession of Croatia to the EU on 1 July 2013. In 2013, the EU started publishing a Croatian-language version of its official gazette.


title: Croatian language

text: Standard Croatian is the official language of the Republic of Croatia and, along with Standard Bosnian and Standard Serbian, one of three official languages of Bosnia and Herzegovina. It is also official in the regions of Burgenland (Austria), Molise (Italy) and Vojvodina (Serbia). Additionally, it has co-official status alongside Romanian in the communes of Carașova and Lupac, Romania. In these localities, Croats or Krashovani make up the majority of the population, and education, signage and access to public administration and the justice system are provided in Croatian, alongside Romanian.


title: Croatian language

text: Croatian is officially used and taught at all the universities in Croatia, and at the University of Mostar in Bosnia and Herzegovina.


title: Croatian language

text: There is no regulatory body that determines the proper usage of Croatian. The current standard language is generally laid out in the grammar books and dictionaries used in education, such as the school curriculum prescribed by the Ministry of Education and the university programmes of the Faculty of Philosophy at the four main universities. In 2013, a "Hrvatski pravopis" by the Institute of Croatian Language and Linguistics received an official sole seal of approval from the Ministry of Education.


title: Croatian language

text: Also notable are the recommendations of Matica hrvatska, the national publisher and promoter of Croatian heritage, and the Lexicographical institute Miroslav Krleža, as well as the Croatian Academy of Sciences and Arts.


title: Croatian language

text: Numerous representative Croatian linguistic works were published since the independence of Croatia, among them three voluminous monolingual dictionaries of contemporary Croatian.


title: Spin (physics)

text: Spin is a conserved quantity carried by elementary particles, and thus by composite particles (hadrons) and atomic nuclei.


title: Spin (physics)

text: Spin is one of two types of angular momentum in quantum mechanics, the other being "orbital angular momentum". The orbital angular momentum operator is the quantum-mechanical counterpart to the classical angular momentum of orbital revolution and appears when there is periodic structure to its wavefunction as the angle varies. For photons, spin is the quantum-mechanical counterpart of the polarization of light; for electrons, the spin has no classical counterpart.


title: Spin (physics)

text: The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The existence of the electron spin can also be inferred theoretically from the spin–statistics theorem and from the Pauli exclusion principle—and vice versa, given the particular spin of the electron, one may derive the Pauli exclusion principle.


title: Spin (physics)

text: Spin is described mathematically as a vector for some particles such as photons, and as spinors and bispinors for other particles such as electrons. Spinors and bispinors behave similarly to vectors: they have definite magnitudes and change under rotations; however, they use an unconventional "direction". All elementary particles of a given kind have the same magnitude of spin angular momentum, though its direction may change. These are indicated by assigning the particle a spin quantum number.


title: Spin (physics)

text: The SI unit of spin is the same as classical angular momentum (i.e., N·m·s, J·s, or kg·m·s). In practice, spin is given as a dimensionless spin quantum number by dividing the spin angular momentum by the reduced Planck constant , which has the same dimensions as angular momentum, although this is not the full computation of this value. Very often, the "spin quantum number" is simply called "spin". The fact that it is a quantum number is implicit.


title: Spin (physics)

text: Wolfgang Pauli in 1924 was the first to propose a doubling of the number of available electron states due to a two-valued non-classical "hidden rotation". In 1925, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested the simple physical interpretation of a particle spinning around its own axis, in the spirit of the old quantum theory of Bohr and Sommerfeld. Ralph Kronig anticipated the Uhlenbeck–Goudsmit model in discussion with Hendrik Kramers several months earlier in Copenhagen, but did not publish. The mathematical theory was worked out in depth by Pauli in 1927. When Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it.


title: Spin (physics)

text: As the name suggests, spin was originally conceived as the rotation of a particle around some axis. While the question of whether elementary particles actually rotate is ambiguous (as they appear point-like), this picture is correct insofar as spin obeys the same mathematical laws as quantized angular momenta do; in particular, spin implies that the particle's phase changes with angle. On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta:


title: Spin (physics)

text: The conventional definition of the spin quantum number is , where can be any non-negative integer. Hence the allowed values of are 0, , 1, , 2, etc. The value of for an elementary particle depends only on the type of particle and cannot be altered in any known way (in contrast to the "spin direction" described below). The spin angular momentum of any physical system is quantized. The allowed values of are


title: Spin (physics)

text: where is the Planck constant, and formula_2 is the reduced Planck constant. In contrast, orbital angular momentum can only take on integer values of ; i.e., even-numbered values of .


title: Spin (physics)

text: Those particles with half-integer spins, such as , , , are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons. The two families of particles obey different rules and "broadly" have different roles in the world around us. A key distinction between the two families is that fermions obey the Pauli exclusion principle: that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning, roughly, having the same position, velocity and spin direction). Fermions obey the rules of Fermi–Dirac statistics. In contrast, bosons obey the rules of Bose–Einstein statistics and have no such restriction, so they may "bunch together" in identical states. Also, composite particles can have spins different from their component particles. For example, a helium-4 atom in the ground state has spin 0 and behaves like a boson, even though the quarks and electrons which make it up are all fermions.


title: Spin (physics)

text: The spin–statistics theorem splits particles into two groups: bosons and fermions, where bosons obey Bose–Einstein statistics, and fermions obey Fermi–Dirac statistics (and therefore the Pauli exclusion principle). Specifically, the theory states that particles with an integer spin are bosons, while all other particles have half-integer spins and are fermions. As an example, electrons have half-integer spin and are fermions that obey the Pauli exclusion principle, while photons have integer spin and do not. The theorem relies on both quantum mechanics and the theory of special relativity, and this connection between spin and statistics has been called "one of the most important applications of the special relativity theory".


title: Spin (physics)

text: Since elementary particles are point-like, self-rotation is not well-defined for them. However, spin implies that the phase of the particle depends on the angle as formula_3, for rotation of angle "θ" around the axis parallel to the spin "S". This is equivalent to the quantum-mechanical interpretation of momentum as phase dependence in the position, and of orbital angular momentum as phase dependence in the angular position.


title: Spin (physics)

text: Photon spin is the quantum-mechanical description of light polarization, where spin +1 and spin −1 represent two opposite directions of circular polarization. Thus, light of a defined circular polarization consists of photons with the same spin, either all +1 or all −1. Spin represents polarization for other vector bosons as well.


title: Spin (physics)

text: For fermions, the picture is less clear. Angular velocity is equal by Ehrenfest theorem to the derivative of the Hamiltonian to its conjugate momentum, which is the total angular momentum operator . Therefore, if the Hamiltonian "H" is dependent upon the spin "S", "dH"/"dS" is non-zero, and the spin causes angular velocity, and hence actual rotation, i.e. a change in the phase-angle relation over time. However, whether this holds for free electron is ambiguous, since for an electron, "S" is constant, and therefore it is a matter of interpretation whether the Hamiltonian includes such a term. Nevertheless, spin appears in the Dirac equation, and thus the relativistic Hamiltonian of the electron, treated as a Dirac field, can be interpreted as including a dependence in the spin "S". Under this interpretation, free electrons also self-rotate, with the Zitterbewegung effect understood as this rotation.


title: Spin (physics)

text: Particles with spin can possess a magnetic dipole moment, just like a rotating electrically charged body in classical electrodynamics. These magnetic moments can be experimentally observed in several ways, e.g. by the deflection of particles by inhomogeneous magnetic fields in a Stern–Gerlach experiment, or by measuring the magnetic fields generated by the particles themselves.


title: Spin (physics)

text: The intrinsic magnetic moment of a spin- particle with charge , mass , and spin angular momentum , is


title: Spin (physics)

text: where the dimensionless quantity is called the spin -factor. For exclusively orbital rotations it would be 1 (assuming that the mass and the charge occupy spheres of equal radius).


title: Spin (physics)

text: The electron, being a charged elementary particle, possesses a nonzero magnetic moment. One of the triumphs of the theory of quantum electrodynamics is its accurate prediction of the electron -factor, which has been experimentally determined to have the value , with the digits in parentheses denoting measurement uncertainty in the last two digits at one standard deviation. The value of 2 arises from the Dirac equation, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of ... arises from the electron's interaction with the surrounding electromagnetic field, including its own field.


title: Spin (physics)

text: Composite particles also possess magnetic moments associated with their spin. In particular, the neutron possesses a non-zero magnetic moment despite being electrically neutral. This fact was an early indication that the neutron is not an elementary particle. In fact, it is made up of quarks, which are electrically charged particles. The magnetic moment of the neutron comes from the spins of the individual quarks and their orbital motions.


title: Spin (physics)

text: Neutrinos are both elementary and electrically neutral. The minimally extended Standard Model that takes into account non-zero neutrino masses predicts neutrino magnetic moments of:


title: Spin (physics)

text: where the are the neutrino magnetic moments, are the neutrino masses, and is the Bohr magneton. New physics above the electroweak scale could, however, lead to significantly higher neutrino magnetic moments. It can be shown in a model-independent way that neutrino magnetic moments larger than about 10  are "unnatural" because they would also lead to large radiative contributions to the neutrino mass. Since the neutrino masses are known to be at most about 1 eV, the large radiative corrections would then have to be "fine-tuned" to cancel each other, to a large degree, and leave the neutrino mass small. The measurement of neutrino magnetic moments is an active area of research. Experimental results have put the neutrino magnetic moment at less than  times the electron's magnetic moment.


title: Spin (physics)

text: On the other hand elementary particles with spin but without electric charge, such as a photon or a Z boson, do not have a magnetic moment.


title: Spin (physics)

text: In ordinary materials, the magnetic dipole moments of individual atoms produce magnetic fields that cancel one another, because each dipole points in a random direction, with the overall average being very near zero. Ferromagnetic materials below their Curie temperature, however, exhibit magnetic domains in which the atomic dipole moments spontaneously align locally, producing a macroscopic, non-zero magnetic field from the domain. These are the ordinary "magnets" with which we are all familiar.


title: Spin (physics)

text: In paramagnetic materials, the magnetic dipole moments of individual atoms will partially align with an externally applied magnetic field. In diamagnetic materials, on the other hand, the magnetic dipole moments of individual atoms align oppositely to any externally applied magnetic field, even if it requires energy to do so.


title: Spin (physics)

text: The study of the behavior of such "spin models" is a thriving area of research in condensed matter physics. For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction. These models have many interesting properties, which have led to interesting results in the theory of phase transitions.


title: Spin (physics)

text: In classical mechanics, the angular momentum of a particle possesses not only a magnitude (how fast the body is rotating), but also a direction (either up or down on the axis of rotation of the particle). Quantum-mechanical spin also contains information about direction, but in a more subtle form. Quantum mechanics states that the component of angular momentum for a spin-"s" particle measured along any direction can only take on the values


title: Spin (physics)

text: where is the spin component along the -th axis (either , , or ), is the spin projection quantum number along the -th axis, and is the principal spin quantum number (discussed in the previous section). Conventionally the direction chosen is the  axis:


title: Spin (physics)

text: One can see that there are possible values of . The number "" is the multiplicity of the spin system. For example, there are only two possible values for a spin- particle: and . These correspond to quantum states in which the spin component is pointing in the +"z" or −"z" directions respectively, and are often referred to as "spin up" and "spin down". For a spin- particle, like a delta baryon, the possible values are +, +, −, −.