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102-414: Vehicles can use propellants to move by ejecting a propellant backwards which creates an opposite force that moves the vehicle forward. Projectiles can use propellants that are expanding gases which provide the motive force to set the projectile in motion. Aerosol cans use propellants which are fluids that are compressed so that when the propellant is allowed to escape by releasing a valve, the energy stored by

204-419: A Δ v {\displaystyle \Delta v} of 9.8 m/s each second). If the possible rate is only g {\displaystyle g} or less, the maneuver can not be carried out at all with this engine. The power is given by where F {\displaystyle F} is the thrust and a {\displaystyle a} the acceleration due to it. Thus

306-478: A Δ v {\displaystyle \Delta v} of ca. 9.5 km/s (mostly for the speed to be acquired), but if the engine could produce Δ v {\displaystyle \Delta v} at a rate of only slightly more than g , it would be a slow launch requiring altogether a very large Δ v {\displaystyle \Delta v} (think of hovering without making any progress in speed or altitude, it would cost

408-470: A nozzle . The exhaust material may be a gas , liquid , plasma , or a solid . In powered aircraft without propellers such as jets , the propellant is usually the product of the burning of fuel with atmospheric oxygen so that the resulting propellant product has more mass than the fuel carried on the vehicle. Proposed photon rockets would use the relativistic momentum of photons to create thrust. Even though photons do not have mass, they can still act as

510-410: A nozzle . The exhaust material may be a gas , liquid , plasma , or a solid . In powered aircraft without propellers such as jets , the propellant is usually the product of the burning of fuel with atmospheric oxygen so that the resulting propellant product has more mass than the fuel carried on the vehicle. The propellant or fuel may also simply be a compressed fluid, with the potential energy that

612-464: A plasma which is used as the propellant. They use a nozzle to direct the energized propellant. The nozzle itself may be composed simply of a magnetic field. Low molecular weight gases (e.g. hydrogen, helium, ammonia) are preferred propellants for this kind of system. Electromagnetic thrusters use ions as the propellant, which are accelerated by the Lorentz force or by magnetic fields, either of which

714-486: A 19 million cubic foot solution-mined salt cavern to store air at up to 1100 psi. Although the compression phase is approximately 82% efficient, the expansion phase requires the combustion of natural gas at one-third the rate of a gas turbine producing the same amount of electricity at 54% efficiency. In 2012, General Compression completed construction of a 2-MW near-isothermal project in Gaines County, Texas ,

816-483: A broad variety of payloads. Aerosol sprays , in which a liquid is ejected as a spray, include paints, lubricants, degreasers, and protective coatings; deodorants and other personal care products; cooking oils. Some liquid payloads are not sprayed due to lower propellant pressure and/or viscous payload, as with whipped cream and shaving cream or shaving gel. Low-power guns, such as BB guns , paintball guns, and airsoft guns, have solid projectile payloads. Uniquely, in

918-464: A certain limit, as do the stresses induced on the storage vessels. The storage vessel is often a cavern created by solution mining (salt is dissolved in water for extraction) or by using an abandoned mine ; use of porous and permeable rock formations (rocks that have interconnected holes, through which liquid or air can pass), such as those in which reservoirs of natural gas are found, has also been studied. In some cases, an above-ground pipeline

1020-400: A compressor, rather than by a chemical reaction. The pressures and energy densities that can be achieved, while insufficient for high-performance rocketry and firearms, are adequate for most applications, in which case compressed fluids offer a simpler, safer, and more practical source of propellant pressure. A compressed fluid propellant may simply be a pressurized gas, or a substance which is

1122-402: A computer. All reaction engines lose some energy, mostly as heat. Different reaction engines have different efficiencies and losses. For example, rocket engines can be up to 60–70% energy efficient in terms of accelerating the propellant. The rest is lost as heat and thermal radiation, primarily in the exhaust. Reaction engines are more energy efficient when they emit their reaction mass when

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1224-426: A computer. Some effects such as Oberth effect can only be significantly utilised by high thrust engines such as rockets; i.e., engines that can produce a high g-force (thrust per unit mass, equal to delta-v per unit time). In the ideal case m 1 {\displaystyle m_{1}} is useful payload and m 0 − m 1 {\displaystyle m_{0}-m_{1}}

1326-540: A cost of $ 208 million, operating in 2024 with 64% efficiency. In 2009, the US Department of Energy awarded $ 24.9 million in matching funds for phase one of a 300-MW, $ 356 million Pacific Gas and Electric Company installation using a saline porous rock formation being developed near Bakersfield in Kern County, California . The goals of the project were to build and validate an advanced design. In 2010,

1428-431: A gas at atmospheric pressure, but stored under pressure as a liquid. In applications in which a large quantity of propellant is used, such as pressure washing and airbrushing , air may be pressurized by a compressor and used immediately. Additionally, a hand pump to compress air can be used for its simplicity in low-tech applications such as atomizers , plant misters and water rockets . The simplest examples of such

1530-418: A mission, for example, when launching from or landing on a planet, the effects of gravitational attraction and any atmospheric drag must be overcome by using fuel. It is typical to combine the effects of these and other effects into an effective mission delta-v . For example, a launch mission to low Earth orbit requires about 9.3–10 km/s delta-v. These mission delta-vs are typically numerically integrated on

1632-418: A mission, for example, when launching from or landing on a planet, the effects of gravitational attraction and any atmospheric drag must be overcome by using fuel. It is typical to combine the effects of these and other effects into an effective mission delta-v . For example, a launch mission to low Earth orbit requires about 9.3–10 km/s delta-v. These mission delta-vs are typically numerically integrated on

1734-402: A modest pressure. This pressure is high enough to provide useful propulsion of the payload (e.g. aerosol paint, deodorant, lubricant), but is low enough to be stored in an inexpensive metal can, and to not pose a safety hazard in case the can is ruptured. The mixture of liquid and gaseous propellant inside the can maintains a constant pressure, called the liquid's vapor pressure . As the payload

1836-442: A propellant because they move at relativistic speed, i.e., the speed of light. In this case Newton's third Law of Motion is inadequate to model the physics involved and relativistic physics must be used. In chemical rockets, chemical reactions are used to produce energy which creates movement of a fluid which is used to expel the products of that chemical reaction (and sometimes other substances) as propellants. For example, in

1938-608: A similar approach, substituting seawater for air. The venturi warms the exhaust of the preceding stage and admits this preheated air to the following stage. This approach was widely adopted in various compressed-air vehicles such as H. K. Porter, Inc. 's mining locomotives and trams. Here, the heat of compression is effectively stored in the atmosphere (or sea) and returned later on. Compression can be done with electrically-powered turbo-compressors and expansion with turbo-expanders or air engines driving electrical generators to produce electricity. Air storage vessels vary in

2040-488: A simple hydrogen/oxygen engine, hydrogen is burned (oxidized) to create H 2 O and the energy from the chemical reaction is used to expel the water (steam) to provide thrust. Often in chemical rocket engines, a higher molecular mass substance is included in the fuel to provide more reaction mass. Rocket propellant may be expelled through an expansion nozzle as a cold gas, that is, without energetic mixing and combustion, to provide small changes in velocity to spacecraft by

2142-685: A smaller scale, such as exploited by air cars and air-driven locomotives , and can use high-strength (e.g., carbon-fiber ) air-storage tanks. In order to retain the energy stored in compressed air, this tank should be thermally isolated from the environment; otherwise, the energy stored will escape in the form of heat, because compressing air raises its temperature. Citywide compressed air energy systems for delivering mechanical power directly via compressed air have been built since 1870. Cities such as Paris , France; Birmingham , England; Dresden , Rixdorf , and Offenbach , Germany; and Buenos Aires , Argentina, installed such systems. Victor Popp constructed

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2244-413: A specific impulse that is both high and fixed such as Ion thrusters have exhaust velocities that can be enormously higher than this ideal, and thus end up powersource limited and give very low thrust. Where the vehicle performance is power limited, e.g. if solar power or nuclear power is used, then in the case of a large v e {\displaystyle v_{e}} the maximum acceleration

2346-429: A stationary engine does no useful work. Exhausting the entire usable propellant of a spacecraft through the engines in a straight line in free space would produce a net velocity change to the vehicle; this number is termed delta-v ( Δ v {\displaystyle \Delta v} ). If the exhaust velocity is constant then the total Δ v {\displaystyle \Delta v} of

2448-451: A system are squeeze bottles for such liquids as ketchup and shampoo. However, compressed gases are impractical as stored propellants if they do not liquify inside the storage container, because very high pressures are required in order to store any significant quantity of gas, and high-pressure gas cylinders and pressure regulators are expensive and heavy. Liquefied gas propellants are gases at atmospheric pressure, but become liquid at

2550-549: A target of 70% efficiency by using 600 °C (1,112 °F) air at 100 bars of pressure. This project was delayed for undisclosed reasons until at least 2016. Storelectric Ltd planned to build a 40-MW 100% renewable energy pilot plant in Cheshire , UK, with 800 MWh of storage capacity (2017). Hydrostor completed the first commercial A-CAES system in Goderich, Ontario , supplying service with 2.2MW / 10MWh storage to

2652-403: A thrust to weight ratio of more than one. To do this with the ion or more theoretical electrical drives, the engine would have to be supplied with one to several gigawatts of power, equivalent to a major metropolitan generating station . From the table it can be seen that this is clearly impractical with current power sources. Alternative approaches include some forms of laser propulsion , where

2754-497: A variety of usually ionized propellants, including atomic ions, plasma, electrons, or small droplets or solid particles as propellant. If the acceleration is caused mainly by the Coulomb force (i.e. application of a static electric field in the direction of the acceleration) the device is considered electrostatic. The types of electrostatic drives and their propellants: These are engines that use electromagnetic fields to generate

2856-476: A vehicle can be calculated using the rocket equation, where M is the mass of propellant, P is the mass of the payload (including the rocket structure), and v e {\displaystyle v_{e}} is the velocity of the rocket exhaust . This is known as the Tsiolkovsky rocket equation : For historical reasons, as discussed above, v e {\displaystyle v_{e}}

2958-480: Is Conclusions: These results apply for a fixed exhaust speed. Due to the Oberth effect and starting from a nonzero speed, the required potential energy needed from the propellant may be less than the increase in energy in the vehicle and payload. This can be the case when the reaction mass has a lower speed after being expelled than before – rockets are able to liberate some or all of the initial kinetic energy of

3060-486: Is 0%, then it is totally adiabatic; with an efficiency of 100%, it is totally isothermal. Typically with a near-isothermal process, an isothermal efficiency of 90–95% can be expected. One implementation of isothermal CAES uses high-, medium-, and low-pressure pistons in series. Each stage is followed by an airblast venturi pump that draws ambient air over an air-to-air (or air-to-seawater) heat exchanger between each expansion stage. Early compressed-air torpedo designs used

3162-498: Is a constant pressure outside of the vessel, which is equal to the starting pressure p A {\displaystyle p_{A}} , the positive work of the outer pressure reduces the exploitable energy (negative value). This adds a term to the equation above: Reaction engine A reaction engine is an engine or motor that produces thrust by expelling reaction mass (reaction propulsion), in accordance with Newton's third law of motion . This law of motion

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3264-627: Is achieved, the exhaust stops in space and has no kinetic energy; and the propulsive efficiency is 100% all the energy ends up in the vehicle (in principle such a drive would be 100% efficient, in practice there would be thermal losses from within the drive system and residual heat in the exhaust). However, in most cases this uses an impractical quantity of propellant, but is a useful theoretical consideration. Some drives (such as VASIMR or electrodeless plasma thruster ) actually can significantly vary their exhaust velocity. This can help reduce propellant usage and improve acceleration at different stages of

3366-422: Is approximately 3000 m/s, using a Hohmann transfer orbit . For the sake of argument, assume the following thrusters are options to be used: Observe that the more fuel-efficient engines can use far less fuel; their mass is almost negligible (relative to the mass of the payload and the engine itself) for some of the engines. However, these require a large total amount of energy. For Earth launch, engines require

3468-523: Is called a reaction engine . Although the term "propellant" is often used in chemical rocket design to describe a combined fuel/propellant, propellants should not be confused with the fuel that is used by an engine to produce the energy that expels the propellant. Even though the byproducts of substances used as fuel are also often used as a reaction mass to create the thrust, such as with a chemical rocket engine, propellant and fuel are two distinct concepts. In electrically powered spacecraft , electricity

3570-456: Is commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force." Examples include jet engines , rocket engines , pump-jets , and more uncommon variations such as Hall effect thrusters , ion drives , mass drivers , and nuclear pulse propulsion . The discovery of the reaction engine has been attributed to the Romanian inventor Alexandru Ciurcu and to

3672-440: Is depleted, the propellant vaporizes to fill the internal volume of the can. Liquids are typically 500-1000x denser than their corresponding gases at atmospheric pressure; even at the higher pressure inside the can, only a small fraction of its volume needs to be propellant in order to eject the payload and replace it with vapor. Vaporizing the liquid propellant to gas requires some energy, the enthalpy of vaporization , which cools

3774-418: Is for the ideal case again, with no energy lost on heat, etc. The latter causes a reduction of thrust, so it is a disadvantage even when the objective is to lose energy (deceleration). If the energy is produced by the mass itself, as in a chemical rocket, the fuel value has to be v e 2 / 2 {\displaystyle \scriptstyle {v_{\text{e}}^{2}/2}} , where for

3876-436: Is generated by electricity: Nuclear reactions may be used to produce the energy for the expulsion of the propellants. Many types of nuclear reactors have been used/proposed to produce electricity for electrical propulsion as outlined above. Nuclear pulse propulsion uses a series of nuclear explosions to create large amounts of energy to expel the products of the nuclear reaction as the propellant. Nuclear thermal rockets use

3978-408: Is inadequate to model the physics involved and relativistic physics must be used. In chemical rockets, chemical reactions are used to produce energy which creates movement of a fluid which is used to expel the products of that chemical reaction (and sometimes other substances) as propellants. For example, in a simple hydrogen/oxygen engine, hydrogen is burned (oxidized) to create H 2 O and

4080-399: Is inversely proportional to it. Hence the time to reach a required delta-v is proportional to v e {\displaystyle v_{e}} . Thus the latter should not be too large. On the other hand, if the exhaust velocity can be made to vary so that at each instant it is equal and opposite to the vehicle velocity then the absolute minimum energy usage is achieved. When this

4182-410: Is no exergy loss in the heat transfer process, and so the compression work can be completely recovered as expansion work: 100% storage efficiency. However, in practice, there is always a temperature difference in any heat transfer process, and so all practical energy storage obtains efficiencies lower than 100%. To estimate the compression/expansion work in an isothermal process, it may be assumed that

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4284-422: Is reaction mass (this corresponds to empty tanks having no mass, etc.). The energy required can simply be computed as This corresponds to the kinetic energy the expelled reaction mass would have at a speed equal to the exhaust speed. If the reaction mass had to be accelerated from zero speed to the exhaust speed, all energy produced would go into the reaction mass and nothing would be left for kinetic energy gain by

4386-547: Is relatively simple, the burning of fuel adds to the cost of the recovered electrical energy and compromises the ecological benefits associated with most renewable energy sources. Nevertheless, this is thus far the only system that has been implemented commercially. The McIntosh, Alabama , CAES plant requires 2.5 MJ of electricity and 1.2 MJ lower heating value (LHV) of gas for each MJ of energy output, corresponding to an energy recovery efficiency of about 27%. A General Electric 7FA 2x1 combined cycle plant, one of

4488-445: Is roughly linear , and little reaction mass is needed. If Δ v {\displaystyle \Delta v} is comparable to v e , then there needs to be about twice as much fuel as combined payload and structure (which includes engines, fuel tanks, and so on). Beyond this, the growth is exponential; speeds much higher than the exhaust velocity require very high ratios of fuel mass to payload and structural mass. For

4590-439: Is sometimes written as where I sp {\displaystyle I_{\text{sp}}} is the specific impulse of the rocket, measured in seconds, and g 0 {\displaystyle g_{0}} is the gravitational acceleration at sea level. For a high delta-v mission, the majority of the spacecraft's mass needs to be reaction mass. Because a rocket must carry all of its reaction mass, most of

4692-431: Is stored in the compressed fluid used to expel the fluid as the propellant. The energy stored in the fluid was added to the system when the fluid was compressed, such as compressed air . The energy applied to the pump or thermal system that is used to compress the air is stored until it is released by allowing the propellant to escape. Compressed fluid may also be used only as energy storage along with some other substance as

4794-406: Is the absolute pressure , V A {\displaystyle V_{A}} is the (unknown) volume of gas compressed, V B {\displaystyle V_{B}} is the volume of the vessel, n {\displaystyle n} is the amount of substance of gas (mol), and R {\displaystyle R} is the ideal gas constant . If there

4896-405: Is the exhaust velocity), which is simply the energy to accelerate the exhaust. Comparing the rocket equation (which shows how much energy ends up in the final vehicle) and the above equation (which shows the total energy required) shows that even with 100% engine efficiency, certainly not all energy supplied ends up in the vehicle – some of it, indeed usually most of it, ends up as kinetic energy of

4998-507: Is the management of thermal energy, since the compression of air leads to an unwanted temperature increase that not only reduces operational efficiency but can also lead to damage. The main difference between various architectures lies in thermal engineering. On the other hand, small-scale systems have long been used for propulsion of mine locomotives . Contrasted with traditional batteries, systems can store energy for longer periods of time and have less upkeep. Compression of air creates heat;

5100-432: Is the specific energy of the rocket (potential plus kinetic energy) and Δ v {\displaystyle \Delta v} is a separate variable, not just the change in v {\displaystyle v} . In the case of using the rocket for deceleration; i.e., expelling reaction mass in the direction of the velocity, v {\displaystyle v} should be taken negative. The formula

5202-409: Is used to accelerate the propellant. An electrostatic force may be used to expel positive ions, or the Lorentz force may be used to expel negative ions and electrons as the propellant. Electrothermal engines use the electromagnetic force to heat low molecular weight gases (e.g. hydrogen, helium, ammonia) into a plasma and expel the plasma as propellant. In the case of a resistojet rocket engine,

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5304-409: Is used to accelerate the propellant. An electrostatic force may be used to expel positive ions, or the Lorentz force may be used to expel negative ions and electrons as the propellant. Electrothermal engines use the electromagnetic force to heat low molecular weight gases (e.g. hydrogen, helium, ammonia) into a plasma and expel the plasma as propellant. In the case of a resistojet rocket engine,

5406-403: Is usually made up of a series of parallel fins. As the gas is compressed, the heat of compression is rapidly transferred to the thermal mass, so the gas temperature is stabilized. An external cooling circuit is then used to maintain the temperature of the thermal mass. The isothermal efficiency (Z) is a measure of where the process lies between an adiabatic and isothermal process. If the efficiency

5508-504: The French journalist Just Buisson  [ fr ; ro ] . For all reaction engines that carry on-board propellant (such as rocket engines and electric propulsion drives) some energy must go into accelerating the reaction mass. Every engine wastes some energy, but even assuming 100% efficiency, the engine needs energy amounting to (where M is the mass of propellent expended and V e {\displaystyle V_{e}}

5610-753: The Gem project at Rosamond in Kern County, California , was planned to provide 500 MW / 4,000 MWh of storage. The Pecho project in San Luis Obispo, California , was planned to be 400 MW / 3,200 MWh. The Broken Hill project in New South Wales , Australia was 200 MW / 1,600 MWh. In 2023, Alliant Energy announced plans to construct a 200-MWh compressed CO 2 facility based on the Sardinia facility in Columbia County, Wisconsin . It will be

5712-824: The Ontario Grid (2019). It was the first A-CAES system to achieve commercial operation in decades. The European-Union-funded RICAS (adiabatic) project in Austria was to use crushed rock to store heat from the compression process to improve efficiency (2020). The system was expected to achieve 70–80% efficiency. Apex planned a plant for Anderson County, Texas , to go online in 2016. This project has been delayed until at least 2020. Canadian company Hydrostor planned to build four Advance plants in Toronto , Goderich, Angas, and Rosamond (2020). Some included partial heat storage in water, improving efficiency to 65%. As of 2022,

5814-590: The US Department of Energy provided $ 29.4 million in funding to conduct preliminary work on a 150-MW salt-based project being developed by Iberdrola USA in Watkins Glen, New York . The goal is to incorporate smart grid technology to balance renewable intermittent energy sources . The first adiabatic project, a 200-megawatt facility called ADELE, was planned for construction in Germany (2013) with

5916-454: The air is warmer after compression. Expansion removes heat. If no extra heat is added, the air will be much colder after expansion. If the heat generated during compression can be stored and used during expansion, then the efficiency of the storage improves considerably. There are several ways in which a CAES system can deal with heat. Air storage can be adiabatic , diabatic, isothermal , or near-isothermal. Adiabatic storage continues to store

6018-434: The air must be substantially re-heated prior to expansion in the turbine to power a generator . This reheating can be accomplished with a natural-gas -fired burner for utility -grade storage or with a heated metal mass. As recovery is often most needed when renewable sources are quiescent, the fuel must be burned to make up for the wasted heat. This degrades the efficiency of the storage-recovery cycle. While this approach

6120-563: The burning of the fuel and, as a consequence, thrust vs time profile. There are three types of burns that can be achieved with different grains. There are four different types of solid fuel/propellant compositions: In rockets, three main liquid bipropellant combinations are used: cryogenic oxygen and hydrogen, cryogenic oxygen and a hydrocarbon, and storable propellants. Propellant combinations used for liquid propellant rockets include: Common monopropellant used for liquid rocket engines include: Electrically powered reactive engines use

6222-408: The case of a gas duster ("canned air"), the only payload is the velocity of the propellant vapor itself. Compressed-air energy storage Compressed-air-energy storage (CAES) is a way to store energy for later use using compressed air . At a utility scale, energy generated during periods of low demand can be released during peak load periods. The first utility-scale CAES project

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6324-744: The compressed air obeys the ideal gas law : For a process from an initial state A to a final state B , with absolute temperature T = T A = T B {\displaystyle T=T_{A}=T_{B}} constant, one finds the work required for compression (negative) or done by the expansion (positive) to be where p V = p A V A = p B V B {\displaystyle pV=p_{A}V_{A}=p_{B}V_{B}} , and so V B V A = p A p B {\displaystyle {\frac {V_{B}}{V_{A}}}={\frac {p_{A}}{p_{B}}}} . Here p {\displaystyle p}

6426-403: The compressed propellant is simply heated using resistive heating as it is expelled to create more thrust. In chemical rockets and aircraft, fuels are used to produce an energetic gas that can be directed through a nozzle , thereby producing thrust. In rockets, the burning of rocket fuel produces an exhaust, and the exhausted material is usually expelled as a propellant under pressure through

6528-403: The compressed propellant is simply heated using resistive heating as it is expelled to create more thrust. In chemical rockets and aircraft, fuels are used to produce an energetic gas that can be directed through a nozzle , thereby producing thrust. In rockets, the burning of rocket fuel produces an exhaust, and the exhausted material is usually expelled as a propellant under pressure through

6630-437: The compression moves the propellant out of the can and that propellant forces the aerosol payload out along with the propellant. Compressed fluid may also be used as a simple vehicle propellant, with the potential energy that is stored in the compressed fluid used to expel the fluid as the propellant. The energy stored in the fluid was added to the system when the fluid was compressed, such as compressed air . The energy applied to

6732-570: The cost of the vessel itself. A different approach consists of burying a large bag buried under several meters of sand instead of water. Plants operate on a peak-shaving daily cycle, charging at night and discharging during the day. Heating the compressed air using natural gas or geothermal heat to increase the amount of energy being extracted has been studied by the Pacific Northwest National Laboratory . Compressed-air energy storage can also be employed on

6834-651: The disadvantage of being flammable . Nitrous oxide and carbon dioxide are also used as propellants to deliver foodstuffs (for example, whipped cream and cooking spray ). Medicinal aerosols such as asthma inhalers use hydrofluoroalkanes (HFA): either HFA 134a (1,1,1,2,-tetrafluoroethane) or HFA 227 (1,1,1,2,3,3,3-heptafluoropropane) or combinations of the two. More recently, liquid hydrofluoroolefin (HFO) propellants have become more widely adopted in aerosol systems due to their relatively low vapor pressure, low global warming potential (GWP), and nonflammability. The practicality of liquified gas propellants allows for

6936-399: The energy from the chemical reaction is used to expel the water (steam) to provide thrust. Often in chemical rocket engines, a higher molecular mass substance is included in the fuel to provide more reaction mass. Rocket propellant may be expelled through an expansion nozzle as a cold gas, that is, without energetic mixing and combustion, to provide small changes in velocity to spacecraft by

7038-486: The energy produced by compression and returns it to the air as it is expanded to generate power. This is a subject of an ongoing study, with no utility-scale plants as of 2015. The theoretical efficiency of adiabatic storage approaches 100% with perfect insulation, but in practice, round trip efficiency is expected to be 70%. Heat can be stored in a solid such as concrete or stone, or in a fluid such as hot oil (up to 300 °C) or molten salt solutions (600 °C). Storing

7140-481: The energy produced by the fuel minus the energy gain of the reaction mass. The larger the speed of the rocket, the smaller the energy gain of the reaction mass; if the rocket speed is more than half of the exhaust speed the reaction mass even loses energy on being expelled, to the benefit of the energy gain of the rocket; the larger the speed of the rocket, the larger the energy loss of the reaction mass. We have where ϵ {\displaystyle \epsilon }

7242-407: The energy required is 50 MJ per kg reaction mass, only 20 MJ is used for the increase in speed of the reaction mass. The remaining 30 MJ is the increase of the kinetic energy of the rocket and payload. In general: Thus the specific energy gain of the rocket in any small time interval is the energy gain of the rocket including the remaining fuel, divided by its mass, where the energy gain is equal to

7344-399: The environment. In practice, neither of these perfect thermodynamic cycles is obtainable, as some heat losses are unavoidable, leading to a near-isothermal process. Near-isothermal compression (and expansion) is a process in which a gas is compressed in very close proximity to a large incompressible thermal mass such as a heat-absorbing and -releasing structure (HARS) or a water spray. A HARS

7446-423: The exhaust. If the specific impulse ( I s p {\displaystyle I_{sp}} ) is fixed, for a mission delta-v, there is a particular I s p {\displaystyle I_{sp}} that minimises the overall energy used by the rocket. This comes to an exhaust velocity of about ⅔ of the mission delta-v (see the energy computed from the rocket equation ). Drives with

7548-554: The first of its kind in the United States. Compressed air energy storage may be stored in undersea caves in Northern Ireland . In order to achieve a near- thermodynamically-reversible process so that most of the energy is saved in the system and can be retrieved, and losses are kept negligible, a near-reversible isothermal process or an isentropic process is desired. In an isothermal compression process,

7650-499: The first systems to power clocks by sending a pulse of air every minute to change their pointer arms. They quickly evolved to deliver power to homes and industries. As of 1896, the Paris system had 2.2 MW of generation distributed at 550 kPa in 50 km of air pipes for motors in light and heavy industry. Usage was measured in cubic meters. The systems were the main source of house-delivered energy in those days and also powered

7752-400: The flight. However the best energetic performance and acceleration is still obtained when the exhaust velocity is close to the vehicle speed. Proposed ion and plasma drives usually have exhaust velocities enormously higher than that ideal (in the case of VASIMR the lowest quoted speed is around 15 km/s compared to a mission delta-v from high Earth orbit to Mars of about 4 km/s ). For

7854-424: The fuel value also the mass of the oxidizer has to be taken into account. A typical value is v e {\displaystyle v_{\text{e}}} = 4.5 km/s, corresponding to a fuel value of 10.1   MJ/kg. The actual fuel value is higher, but much of the energy is lost as waste heat in the exhaust that the nozzle was unable to extract. The required energy E {\displaystyle E}

7956-543: The gas in the system is kept at a constant temperature throughout. This necessarily requires an exchange of heat with the gas; otherwise, the temperature would rise during charging and drop during discharge. This heat exchange can be achieved by heat exchangers (intercooling) between subsequent stages in the compressor, regulator, and tank. To avoid wasted energy, the intercoolers must be optimized for high heat transfer and low pressure drop. Smaller compressors can approximate isothermal compression even without intercooling, due to

8058-412: The heat in hot water may yield an efficiency around 65%. Packed beds have been proposed as thermal storage units for adiabatic systems. A study numerically simulated an adiabatic compressed air energy storage system using packed bed thermal energy storage. The efficiency of the simulated system under continuous operation was calculated to be between 70.5% and 71%. Diabatic storage dissipates much of

8160-461: The heat of a nuclear reaction to heat a propellant. Usually the propellant is hydrogen because the force is a function of the energy irrespective of the mass of the propellant, so the lightest propellant (hydrogen) produces the greatest specific impulse . A photonic reactive engine uses photons as the propellant and their discrete relativistic energy to produce thrust. Compressed fluid or compressed gas propellants are pressurized physically, by

8262-421: The heat of compression with intercoolers (thus approaching isothermal compression) into the atmosphere as waste, essentially wasting the energy used to perform the work of compression. Upon removal from storage, the temperature of this compressed air is the one indicator of the amount of stored energy that remains in this air. Consequently, if the air temperature is too low for the energy recovery process, then

8364-599: The initially-expended reaction mass goes towards accelerating reaction mass rather than payload. If the rocket has a payload of mass P , the spacecraft needs to change its velocity by Δ v {\displaystyle \Delta v} , and the rocket engine has exhaust velocity v e , then the reaction mass M which is needed can be calculated using the rocket equation and the formula for I sp {\displaystyle I_{\text{sp}}} : For Δ v {\displaystyle \Delta v} much smaller than v e , this equation

8466-579: The machines of dentists , seamstresses , printing facilities, and bakeries . The first utility-scale diabatic compressed air energy storage project was the 290-megawatt Huntorf plant opened in 1978 in Germany using a salt dome cavern with 580 MWh energy and a 42% efficiency. A 110-megawatt plant with a capacity of 26 hours (2,860 MWh energy) was built in McIntosh, Alabama in 1991. The Alabama facility's $ 65 million cost equals $ 590 per kW of capacity and about $ 23 per kW-hr of storage capacity. It uses

8568-579: The most efficient natural gas plants in operation, uses 1.85 MJ (LHV) of gas per MJ generated, a 54% thermal efficiency . Isothermal compression and expansion approaches attempt to maintain operating temperature by constant heat exchange to the environment. In a reciprocating compressor, this can be achieved by using a finned piston and low cycle speeds. Current challenges in effective heat exchangers mean that they are only practical for low power levels. The theoretical efficiency of isothermal energy storage approaches 100% for perfect heat transfer to

8670-400: The newly synthesized bishomocubane based compounds are under consideration in the research stage as both solid and liquid propellants of the future. Solid fuel/propellants are used in forms called grains . A grain is any individual particle of fuel/propellant regardless of the size or shape. The shape and size of a grain determines the burn time, amount of gas, and rate of produced energy from

8772-528: The propellant). Chlorofluorocarbons (CFCs) were once often used as propellants, but since the Montreal Protocol came into force in 1989, they have been replaced in nearly every country due to the negative effects CFCs have on Earth's ozone layer . The most common replacements of CFCs are mixtures of volatile hydrocarbons , typically propane , n- butane and isobutane . Dimethyl ether (DME) and methyl ethyl ether are also used. All these have

8874-414: The propellant, such as with a water rocket , where the energy stored in the compressed air is the fuel and the water is the propellant. Proposed photon rockets would use the relativistic momentum of photons to create thrust. Even though photons do not have mass, they can still act as a propellant because they move at relativistic speed, i.e., the speed of light. In this case Newton's third Law of Motion

8976-424: The propellant. Also, for a given objective such as moving from one orbit to another, the required Δ v {\displaystyle \Delta v} may depend greatly on the rate at which the engine can produce Δ v {\displaystyle \Delta v} and maneuvers may even be impossible if that rate is too low. For example, a launch to Low Earth orbit (LEO) normally requires

9078-410: The pump or thermal system that is used to compress the air is stored until it is released by allowing the propellant to escape. Compressed fluid may also be used only as energy storage along with some other substance as the propellant, such as with a water rocket , where the energy stored in the compressed air is the fuel and the water is the propellant. In electrically powered spacecraft , electricity

9180-420: The relatively high ratio of surface area to volume of the compression chamber and the resulting improvement in heat dissipation from the compressor body itself. When one obtains perfect isothermal storage (and discharge), the process is said to be "reversible". This requires that the heat transfer between the surroundings and the gas occur over an infinitesimally small temperature difference. In that case, there

9282-512: The rocket and payload. However, if the rocket already moves and accelerates (the reaction mass is expelled in the direction opposite to the direction in which the rocket moves) less kinetic energy is added to the reaction mass. To see this, if, for example, v e {\displaystyle v_{e}} =10 km/s and the speed of the rocket is 3 km/s, then the speed of a small amount of expended reaction mass changes from 3 km/s forwards to 7 km/s rearwards. Thus, although

9384-409: The storage vessel is positioned hundreds of meters below ground level, and the hydrostatic pressure (head) of the water column above the storage vessel maintains the pressure at the desired level. This configuration allows: On the other hand, the cost of this storage system is higher due to the need to position the storage vessel on the bottom of the chosen water reservoir (often the ocean) and due to

9486-413: The system. This is usually insignificant, although it can sometimes be an unwanted effect of heavy usage (as the system cools, the vapor pressure of the propellant drops). However, in the case of a freeze spray , this cooling contributes to the desired effect (although freeze sprays may also contain other components, such as chloroethane , with a lower vapor pressure but higher enthalpy of vaporization than

9588-416: The theoretically possible thrust per unit power is 2 divided by the specific impulse in m/s. The thrust efficiency is the actual thrust as percentage of this. If, e.g., solar power is used, this restricts a {\displaystyle a} ; in the case of a large v e {\displaystyle v_{\text{e}}} the possible acceleration is inversely proportional to it, hence

9690-399: The thermodynamic conditions of the storage and on the technology used: This storage system uses a chamber with specific boundaries to store large amounts of air. This means from a thermodynamic point of view that this system is a constant-volume and variable-pressure system. This causes some operational problems for the compressors and turbines, so the pressure variations have to be kept below

9792-520: The time to reach a required delta-v is proportional to v e {\displaystyle v_{\text{e}}} ; with 100% efficiency: Examples: Thus v e {\displaystyle v_{\text{e}}} should not be too large. The power to thrust ratio is simply: Thus for any vehicle power P, the thrust that may be provided is: Suppose a 10,000 kg space probe will be sent to Mars. The required Δ v {\displaystyle \Delta v} from LEO

9894-413: The use of cold gas thrusters , usually as maneuvering thrusters. To attain a useful density for storage, most propellants are stored as either a solid or a liquid. A rocket propellant is a mass that is expelled from a vehicle, such as a rocket, in such a way as to create a thrust in accordance with Newton's third law of motion , and "propel" the vehicle forward. The engine that expels the propellant

9996-551: The use of cold gas thrusters , usually as maneuvering thrusters. To attain a useful density for storage, most propellants are stored as either a solid or a liquid. Propellants may be energized by chemical reactions to expel solid, liquid or gas. Electrical energy may be used to expel gases, plasmas, ions, solids or liquids. Photons may be used to provide thrust via relativistic momentum. Propellants that explode in operation are of little practical use currently, although there have been experiments with Pulse Detonation Engines . Also

10098-401: The vehicle is travelling at high speed. This is because the useful mechanical energy generated is simply force times distance, and when a thrust force is generated while the vehicle moves, then: where F is the force and d is the distance moved. Dividing by length of time of motion we get: Hence: where P is the useful power and v is the speed. Hence, v should be as high as possible, and

10200-876: The world's third such project. The project uses no fuel. It appears to have stopped operating in 2016. A 60 MW / 300 MWh facility with 60% efficiency opened in Jiangsu , China, using a salt cavern (2022). A 2.5 MW / 4 MWh compressed CO 2 facility started operating in Sardinia , Italy (2022). In 2022, Zhangjiakou connected the world's first 100-MW "advanced" system to the grid in north China. It uses no fossil fuels , instead adopting supercritical thermal storage, supercritical heat exchange, and high-load compression and expansion technologies. The plant can store 400 MWh with 70.4% efficiency. A 350 MW / 1.4 GWh underground salt cave project started construction in Shangdong at

10302-602: Was in the Huntorf power plant in Elsfleth, Germany , and is still operational as of 2024 . The Huntorf plant was initially developed as a load balancer for fossil-fuel-generated electricity , but the global shift towards renewable energy renewed interest in CAES systems, to help highly intermittent energy sources like photovoltaics and wind satisfy fluctuating electricity demands. One ongoing challenge in large-scale design

10404-536: Was tested as a storage system, giving some good results. Obviously, the cost of the system is higher, but it can be placed wherever the designer chooses, whereas an underground system needs some particular geologic formations (salt domes, aquifers, depleted gas fields, etc.). In this case, the storage vessel is kept at constant pressure, while the gas is contained in a variable-volume vessel. Many types of storage vessels have been proposed, generally relying on liquid displacement to achieve isobaric operation. In such cases,

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