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52-455: The kick stage rocket produces 120 newtons (27 lb f ) of thrust, and has a specific impulse of approximately 320 seconds. It was first used on 21 January 2018 during Rocket Lab's first successful orbital rocket launch, and helped to boost two small CubeSats , the weather and ship-tracking Lemur-2 CubeSats built by the company Spire Global , into a circular orbit. The Curie engine, named after Polish scientist Marie Skłodowska–Curie ,

104-417: A direct measure of the engine's effectiveness in converting propellant mass into forward momentum. The specific impulse in terms of propellant mass spent has units of distance per time, which is a notional velocity called the effective exhaust velocity . This is higher than the actual exhaust velocity because the mass of the combustion air is not being accounted for. Actual and effective exhaust velocity are

156-434: A given propellant, when paired with a given engine, can accelerate its own initial mass at 1 g. The longer it can accelerate its own mass, the more delta-V it delivers to the whole system. In other words, given a particular engine and a mass of a particular propellant, specific impulse measures for how long a time that engine can exert a continuous force (thrust) until fully burning that mass of propellant. A given mass of

208-526: A heavier engine with a higher specific impulse may not be as effective in gaining altitude, distance, or velocity as a lighter engine with a lower specific impulse, especially if the latter engine possesses a higher thrust-to-weight ratio . This is a significant reason for most rocket designs having multiple stages. The first stage is optimised for high thrust to boost the later stages with higher specific impulse into higher altitudes where they can perform more efficiently. The most common unit for specific impulse

260-496: A maximum thrust of 5.7 N (1.3 lbf). Impulse (physics) In classical mechanics , impulse (symbolized by J or Imp ) is the change in momentum of an object. If the initial momentum of an object is p 1 , and a subsequent momentum is p 2 , the object has received an impulse J : J = p 2 − p 1 . {\displaystyle \mathbf {J} =\mathbf {p} _{2}-\mathbf {p} _{1}.} Momentum

312-417: A more energy-dense propellant can burn for a longer duration than some less energy-dense propellant made to exert the same force while burning in an engine. Different engine designs burning the same propellant may not be equally efficient at directing their propellant's energy into effective thrust. For all vehicles, specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by

364-417: A much higher specific impulse than rocket engines. For air-breathing engines, only the fuel mass is counted, not the mass of air passing through the engine. Air resistance and the engine's inability to keep a high specific impulse at a fast burn rate are limiting factors to the propellant consumption rate. If it were not for air resistance and the reduction of propellant during flight, specific impulse would be

416-421: A much larger specific impulse than a rocket; for example a turbofan jet engine may have a specific impulse of 6,000 seconds or more at sea level whereas a rocket would be between 200 and 400 seconds. An air-breathing engine is thus much more propellant efficient than a rocket engine, because the air serves as reaction mass and oxidizer for combustion which does not have to be carried as propellant, and

468-400: A rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, v e . "In actual rocket nozzles, the exhaust velocity is not really uniform over

520-457: Is a step change , and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in videogame physics engines ). Additionally, in rocketry, the term "total impulse" is commonly used and is considered synonymous with the term "impulse". The application of Newton's second law for variable mass allows impulse and momentum to be used as analysis tools for jet - or rocket -propelled vehicles. In

572-430: Is a vector quantity, so impulse is also a vector quantity. Newton’s second law of motion states that the rate of change of momentum of an object is equal to the resultant force F acting on the object: F = p 2 − p 1 Δ t , {\displaystyle \mathbf {F} ={\frac {\mathbf {p} _{2}-\mathbf {p} _{1}}{\Delta t}},} so

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624-484: Is a measure of how efficiently a reaction mass engine, such as a rocket using propellant or a jet engine using fuel, generates thrust . A propulsion system with a higher specific impulse uses the mass of the propellant more efficiently. In the case of a rocket, this means less propellant needed for a given delta- v , so that the vehicle attached to the engine can more efficiently gain altitude and velocity. For engines like cold gas thrusters whose reaction mass

676-467: Is a small liquid-propellant rocket engine designed to release "small satellites from the constricting parameters of primary payload orbits and enables them to fully reach their potential, including faster deployment of small satellite constellations and better positioning for Earth imaging". It is 3D printed. The Electron third stage, which is powered by Curie, is equipped with its own reaction control system, avionics, power, and communication systems. During

728-490: Is also ionized, which would interfere with radio communication with the rocket. Nuclear thermal rocket engines differ from conventional rocket engines in that energy is supplied to the propellants by an external nuclear heat source instead of the heat of combustion . The nuclear rocket typically operates by passing liquid hydrogen gas through an operating nuclear reactor. Testing in the 1960s yielded specific impulses of about 850 seconds (8,340 m/s), about twice that of

780-450: Is also valid for air-breathing jet engines, but is rarely used in practice. (Note that different symbols are sometimes used; for example, c is also sometimes seen for exhaust velocity. While the symbol I sp {\displaystyle I_{\text{sp}}} might logically be used for specific impulse in units of (N·s )/(m·kg); to avoid confusion, it is desirable to reserve this for specific impulse measured in seconds.) It

832-434: Is impractical. Lithium and fluorine are both extremely corrosive, lithium ignites on contact with air, fluorine ignites on contact with most fuels, and hydrogen, while not hypergolic, is an explosive hazard. Fluorine and the hydrogen fluoride (HF) in the exhaust are very toxic, which damages the environment, makes work around the launch pad difficult, and makes getting a launch license that much more difficult. The rocket exhaust

884-493: Is inversely proportional to specific fuel consumption (SFC) by the relationship I sp = 1/( g o ·SFC) for SFC in kg/(N·s) and I sp = 3600/SFC for SFC in lb/(lbf·hr). An example of a specific impulse measured in time is 453 seconds, which is equivalent to an effective exhaust velocity of 4.440 km/s (14,570 ft/s), for the RS-25 engines when operating in a vacuum. An air-breathing jet engine typically has

936-423: Is needed to produce a given thrust for a given time and the more efficient the propellant is. This should not be confused with the physics concept of energy efficiency , which can decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so. Thrust and specific impulse should not be confused. Thrust is the force supplied by the engine and depends on

988-421: Is only the fuel they carry, specific impulse is exactly proportional to the effective exhaust gas velocity. In an atmospheric context, specific impulse can include the contribution to impulse provided by the mass of external air that is accelerated by the engine, such as by fuel combustion or by external propeller. Jet engines and turbofans breathe external air for both combustion and bypass, and therefore have

1040-408: Is proportional to the effective exhaust velocity. A spacecraft without propulsion follows an orbit determined by its trajectory and any gravitational field. Deviations from the corresponding velocity pattern (these are called Δ v ) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change. When an engine is run within the atmosphere, the exhaust velocity

1092-410: Is reduced by atmospheric pressure, in turn reducing specific impulse. This is a reduction in the effective exhaust velocity, versus the actual exhaust velocity achieved in vacuum conditions. In the case of gas-generator cycle rocket engines, more than one exhaust gas stream is present as turbopump exhaust gas exits through a separate nozzle. Calculating the effective exhaust velocity requires averaging

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1144-409: Is related to the thrust , or forward force on the rocket by the equation: F thrust = v e ⋅ m ˙ , {\displaystyle F_{\text{thrust}}=v_{\text{e}}\cdot {\dot {m}},} where m ˙ {\displaystyle {\dot {m}}} is the propellant mass flow rate, which is the rate of decrease of

1196-452: Is that it may be used for rockets, where all the reaction mass is carried on board, as well as airplanes, where most of the reaction mass is taken from the atmosphere. In addition, giving the result as a unit of time makes the result easily comparable between calculations in SI units, imperial units, US customary units or other unit framework. The English unit pound mass is more commonly used than

1248-723: Is the newton second (N⋅s), or the Cupp, and the dimensionally equivalent unit of momentum is the kilogram metre per second (kg⋅m/s). The corresponding English engineering unit is the pound -second (lbf⋅s), and in the British Gravitational System , the unit is the slug -foot per second (slug⋅ft/s). Impulse J produced from time t 1 to t 2 is defined to be J = ∫ t 1 t 2 F d t , {\displaystyle \mathbf {J} =\int _{t_{1}}^{t_{2}}\mathbf {F} \,\mathrm {d} t,} where F

1300-746: Is the change in linear momentum from time t 1 to t 2 . This is often called the impulse-momentum theorem (analogous to the work-energy theorem ). As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. The impulse may be expressed in a simpler form when the mass is constant: J = ∫ t 1 t 2 F d t = Δ p = m v 2 − m v 1 , {\displaystyle \mathbf {J} =\int _{t_{1}}^{t_{2}}\mathbf {F} \,\mathrm {d} t=\Delta \mathbf {p} =m\mathbf {v_{2}} -m\mathbf {v_{1}} ,} where Impulse has

1352-401: Is the product of the average specific gravity of a given propellant mixture and the specific impulse. While less important than the specific impulse, it is an important measure in launch vehicle design, as a low specific impulse implies that bigger tanks will be required to store the propellant, which in turn will have a detrimental effect on the launch vehicle's mass ratio . Specific impulse

1404-1013: Is the resultant force applied from t 1 to t 2 . From Newton's second law , force is related to momentum p by F = d p d t . {\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}.} Therefore, J = ∫ t 1 t 2 d p d t d t = ∫ p 1 p 2 d p = p 2 − p 1 = Δ p , {\displaystyle {\begin{aligned}\mathbf {J} &=\int _{t_{1}}^{t_{2}}{\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}\,\mathrm {d} t\\&=\int _{\mathbf {p} _{1}}^{\mathbf {p} _{2}}\mathrm {d} \mathbf {p} \\&=\mathbf {p} _{2}-\mathbf {p} _{1}=\Delta \mathbf {p} ,\end{aligned}}} where Δ p

1456-478: Is the second, as values are identical regardless of whether the calculations are done in SI , imperial , or US customary units. Nearly all manufacturers quote their engine performance in seconds, and the unit is also useful for specifying aircraft engine performance. The use of metres per second to specify effective exhaust velocity is also reasonably common. The unit is intuitive when describing rocket engines, although

1508-414: Is used, impulse is divided by propellant weight (weight is a measure of force), resulting in units of time (seconds). These two formulations differ from each other by the standard gravitational acceleration ( g 0 ) at the surface of the earth. The rate of change of momentum of a rocket (including its propellant) per unit time is equal to the thrust. The higher the specific impulse, the less propellant

1560-404: The effective exhaust velocity while reducing the actual exhaust velocity. Again, this is because the mass of the air is not counted in the specific impulse calculation, thus attributing all of the thrust momentum to the mass of the fuel component of the exhaust, and omitting the reaction mass, inert gas, and effect of driven fans on overall engine efficiency from consideration. Essentially,

1612-584: The Curie engine. Rocket Lab has also developed a version of the Curie engine with more thrust called HyperCurie. While Curie is pressure-fed , HyperCurie is electric pump-fed . The engine was used on the CAPSTONE lunar mission that launched in June 2022. HyperCurie is set to be used on the upcoming Photon mission to Venus, Venus Life Finder . Specific impulse Specific impulse (usually abbreviated I sp )

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1664-675: The Space Shuttle engines. A variety of other rocket propulsion methods, such as ion thrusters , give much higher specific impulse but with much lower thrust; for example the Hall-effect thruster on the SMART-1 satellite has a specific impulse of 1,640 s (16.1 km/s) but a maximum thrust of only 68 mN (0.015 lbf). The variable specific impulse magnetoplasma rocket (VASIMR) engine currently in development will theoretically yield 20 to 300 km/s (66,000 to 984,000 ft/s), and

1716-408: The actual exhaust speed is much lower, so the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust. While the actual exhaust velocity is lower for air-breathing engines, the effective exhaust velocity is very high for jet engines. This is because the effective exhaust velocity calculation assumes that the carried propellant is providing all

1768-419: The amount of reaction mass flowing through the engine. Specific impulse measures the impulse produced per unit of propellant and is proportional to the exhaust velocity. Thrust and specific impulse are related by the design and propellants of the engine in question, but this relationship is tenuous. For example, LH 2 /LO 2 bipropellant produces higher I sp but lower thrust than RP-1 / LO 2 due to

1820-427: The burned fuel. Next, inert gases in the atmosphere absorb heat from combustion, and through the resulting expansion provide additional thrust. Lastly, for turbofans and other designs there is even more thrust created by pushing against intake air which never sees combustion directly. These all combine to allow a better match between the airspeed and the exhaust speed, which saves energy/propellant and enormously increases

1872-474: The definition of specific impulse as impulse per unit mass of propellant. Specific fuel consumption is inversely proportional to specific impulse and has units of g/(kN·s) or lb/(lbf·h). Specific fuel consumption is used extensively for describing the performance of air-breathing jet engines. Specific impulse, measured in seconds, can be thought of as how many seconds one kilogram of fuel can produce one kilogram of thrust. Or, more precisely, how many seconds

1924-492: The effective exhaust speed of the engines may be significantly different from the actual exhaust speed, especially in gas-generator cycle engines. For airbreathing jet engines , the effective exhaust velocity is not physically meaningful, although it can be used for comparison purposes. Metres per second are numerically equivalent to newton-seconds per kg (N·s/kg), and SI measurements of specific impulse can be written in terms of either units interchangeably. This unit highlights

1976-638: The entire exit cross section and such velocity profiles are difficult to measure accurately. A uniform axial velocity, v e , is assumed for all calculations which employ one-dimensional problem descriptions. This effective exhaust velocity represents an average or mass equivalent velocity at which propellant is being ejected from the rocket vehicle." The two definitions of specific impulse are proportional to one another, and related to each other by: v e = g 0 ⋅ I sp , {\displaystyle v_{\text{e}}=g_{0}\cdot I_{\text{sp}},} where This equation

2028-435: The exhaust gases having a lower density and higher velocity ( H 2 O vs CO 2 and H 2 O). In many cases, propulsion systems with very high specific impulse—some ion thrusters reach 10,000 seconds—produce low thrust. When calculating specific impulse, only propellant carried with the vehicle before use is counted. For a chemical rocket, the propellant mass therefore would include both fuel and oxidizer . In rocketry,

2080-512: The first flight in January 2018 where Curie was tested, the Electron third stage —also referred to as the "kick stage"—coasted for roughly 40 minutes after successfully deploying an Earth-imaging Dove satellite built by the company Planet Labs , then ignited the Curie engine on its first in-space test. After this test, the stage was left in orbit. However, Rocket Lab stated that future launches would have

2132-455: The following equation: F thrust = g 0 ⋅ I sp ⋅ m ˙ , {\displaystyle F_{\text{thrust}}=g_{0}\cdot I_{\text{sp}}\cdot {\dot {m}},} where: I sp in seconds is the amount of time a rocket engine can generate thrust, given a quantity of propellant whose weight is equal to the engine's thrust. The advantage of this formulation

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2184-464: The impulse J delivered by a steady force F acting for time Δ t is: J = F Δ t . {\displaystyle \mathbf {J} =\mathbf {F} \Delta t.} The impulse delivered by a varying force is the integral of the force F with respect to time: J = ∫ F d t . {\displaystyle \mathbf {J} =\int \mathbf {F} \,\mathrm {d} t.} The SI unit of impulse

2236-490: The momentum of engine exhaust includes a lot more than just fuel, but specific impulse calculation ignores everything but the fuel. Even though the effective exhaust velocity for an air-breathing engine seems nonsensical in the context of actual exhaust velocity, this is still useful for comparing absolute fuel efficiency of different engines. A related measure, the density specific impulse , sometimes also referred to as Density Impulse and usually abbreviated as I s d

2288-465: The only reaction mass is the propellant, so the specific impulse is calculated using an alternative method, giving results with units of seconds. Specific impulse is defined as the thrust integrated over time per unit weight -on-Earth of the propellant: I sp = v e g 0 , {\displaystyle I_{\text{sp}}={\frac {v_{\text{e}}}{g_{0}}},} where In rockets, due to atmospheric effects,

2340-414: The reaction mass and all the thrust. Hence effective exhaust velocity is not physically meaningful for air-breathing engines; nevertheless, it is useful for comparison with other types of engines. The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was 542 seconds (5.32 km/s) with a tripropellant of lithium , fluorine , and hydrogen . However, this combination

2392-422: The same in rocket engines operating in a vacuum. The amount of propellant can be measured either in units of mass or weight. If mass is used, specific impulse is an impulse per unit of mass, which dimensional analysis shows to have units of speed, specifically the effective exhaust velocity . As the SI system is mass-based, this type of analysis is usually done in meters per second. If a force-based unit system

2444-487: The same units and dimensions (MLT ) as momentum. In the International System of Units , these are kg ⋅ m/s = N ⋅ s . In English engineering units , they are slug ⋅ ft/s = lbf ⋅ s . The term "impulse" is also used to refer to a fast-acting force or impact . This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. This sort of change

2496-574: The slug, and when using pounds per second for mass flow rate, it is more convenient to express standard gravity as 1 pound-force per pound-mass. Note that this is equivalent to 32.17405 ft/s2, but expressed in more convenient units. This gives: F thrust = I sp ⋅ m ˙ ⋅ ( 1 l b f l b m ) . {\displaystyle F_{\text{thrust}}=I_{\text{sp}}\cdot {\dot {m}}\cdot \left(1\mathrm {\frac {lbf}{lbm}} \right).} In rocketry,

2548-490: The specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity isn't simply a function of the chamber pressure, but is a function of the difference between the interior and exterior of the combustion chamber . Values are usually given for operation at sea level ("sl") or in a vacuum ("vac"). Because of the geocentric factor of g 0 in the equation for specific impulse, many prefer an alternative definition. The specific impulse of

2600-401: The stage deorbited after releasing their payloads to prevent addition to space debris . While Rocket Lab is not known to have specified the monopropellant used by Curie, in 2012 Rocket Lab demonstrated the use of a non-toxic Viscous Liquid Monopropellant (VLM) that it had developed. In August 2020 Rocket Lab indicated that the kick stage uses an unspecified liquid bi-propellant fuel for

2652-415: The two mass flows as well as accounting for any atmospheric pressure. For air-breathing jet engines, particularly turbofans , the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This happens for several reasons. First, a good deal of additional momentum is obtained by using air as reaction mass, such that combustion products in the exhaust have more mass than

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2704-446: The vehicle's mass. A rocket must carry all its propellant with it, so the mass of the unburned propellant must be accelerated along with the rocket itself. Minimizing the mass of propellant required to achieve a given change in velocity is crucial to building effective rockets. The Tsiolkovsky rocket equation shows that for a rocket with a given empty mass and a given amount of propellant, the total change in velocity it can accomplish

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