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commission des sciences et techniques spatiales (fr)[Domaine]
Propulsion (fr)[Domaine]
specific impulse (n.)↕
Specific impulse (usually abbreviated I_{sp}) is a way to describe the efficiency of rocket and jet engines. It represents the derivative of the impulse with respect to amount of propellant used, i.e., the thrust divided by the amount of propellant used per unit time.^{[1]} If the "amount" of propellant is given in terms of mass (such as kilograms), then specific impulse has units of velocity. If it is given in terms of Earthweight (such as kiloponds), then specific impulse has units of time. The conversion constant between the two versions of specific impulse is g.^{[2]} The higher the specific impulse, the lower the propellant flow rate required for a given thrust, and in the case of a rocket the less propellant is needed for a given deltav per the Tsiolkovsky rocket equation.
The actual exhaust velocity is the average speed that the exhaust jet actually leaves the vehicle. The effective exhaust velocity is the speed that the propellant burned per second would have to leave the vehicle to give the same thrust. The two are about the same for a rocket working in a vacuum, but are radically different for an airbreathing jet engine that obtains extra thrust by accelerating air. Specific impulse and effective exhaust velocity are proportional.
Specific impulse is a useful value to compare engines, much like miles per gallon or litres per 100 kilometres is used for cars.^{[3]} A propulsion method with a higher specific impulse is more propellantefficient.^{[1]} Another number that measures the same thing, usually used for air breathing jet engines, is specific fuel consumption. Specific fuel consumption is inversely proportional to specific impulse and effective exhaust velocity.
Contents 
Propellant is normally measured either in units of mass or weight. If mass is used, specific impulse is an impulse per unit mass, which dimensional analysis shows to be a unit of speed, and so specific impulses are often measured in meters per second and are often termed effective exhaust velocity. However, if propellant weight is used instead, an impulse divided by a force (weight) turns out to be a unit of time, and so specific impulses are measured in seconds. These two formulations are both widely used and differ from each other by a factor of g, the dimensioned constant of gravitational acceleration at the surface of the Earth.
Note that the gain of momentum of a rocket (including fuel) per unit time is not equal to the thrust, because the momentum that the fuel has while in the rocket has to be subtracted to the extent that it is used, i.e., the gain of momentum of a rocket per unit time is equal to the thrust, minus the velocity of the rocket multiplied by the amount of fuel used per unit time. (This gain of momentum of the rocket is the negative of the momentum of the exhaust gas.) See also change of impulse of a variable mass.
The higher the specific impulse, the less propellant is needed to produce a given thrust during a given time. In this regard a propellant is more efficient if the specific impulse is higher. This should not be confused with energy efficiency, which can even decrease as specific impulse increases, since propulsion systems that give high specific impulse require high energy to do so.^{[4]}
In addition it is important that thrust and specific impulse not be confused with one another. The specific impulse is a measure of the impulse per unit of propellant that is expended, while thrust is a measure of the momentary or peak force supplied by a particular engine. In many cases, propulsion systems with very high specific impulses—some ion thrusters reach 10,000 seconds—produce low thrusts.^{[5]}
When calculating specific impulse, only propellant that is carried with the vehicle before use is counted. For a chemical rocket the propellant mass therefore would include both fuel and oxidizer; for airbreathing engines only the mass of the fuel is counted, not the mass of air passing through the engine.
Specific Impulse (by weight) 
Specific Impulse (by mass) 
Effective exhaust velocity 
Specific fuel consumption 


SI  =X seconds  =9.8066 X N•s/kg  =9.8066 X m/s  =(101,972/X) g/kN•s 
Imperial units  =X seconds  =X lbf•s/lb  =32.16 X ft/s  =(3,600/X) lb/lbf•h 
By far the most common unit used for specific impulse today is the second, and this is used both in the SI world as well as where English units are used. Its chief advantages are that its units and numerical value are identical everywhere, and essentially everyone understands it. Nearly all manufacturers quote their engine performance in these units and it is also useful for specifying aircraft engine performance.^{[6]}
The effective exhaust velocity in units of m/s is also in reasonably common usage. For rocket engines it is reasonably intuitive, although for many rocket engines the effective exhaust speed is considerably different from the actual exhaust speed due to, for example, fuel and oxidizer that is dumped overboard after powering turbopumps. For airbreathing engines the effective exhaust velocity is not physically meaningful, although it can be used for comparison purposes nevertheless.^{[7]}
The N•s/kg is not uncommonly seen, and is numerically equal to the effective exhaust velocity in m/s (from Newton's second law and the definition of the Newton.)
Another equivalent unit is specific fuel consumption. This has units of g/kN.s or lbf/lb•h and is inversely proportional to specific impulse. Specific fuel consumption is used extensively for describing the performance of airbreathing jet engines.^{[8]}
For all vehicles specific impulse (impulse per unit weightonEarth of propellant) in seconds can be defined by the following equation^{[3]}:
where:
(When working with English units, it is conventional to divide both sides of the equation by g_{0} so that the left hand side of the equation has units of lbs rather than expressing it in poundals.)
This I_{sp} in seconds value is somewhat physically meaningful—if an engine's thrust could be adjusted to equal the initial weight of its propellant (measured at one standard gravity), then I_{sp} is the duration the propellant would last.^{[citation needed]}
The advantage that this formulation has is that it may be used for rockets, where all the reaction mass is carried onboard, as well as aeroplanes, where most of the reaction mass is taken from the atmosphere. In addition, it gives a result that is independent of units used (provided the unit of time used is the second).
In rocketry, where the only reaction mass is the propellant, an equivalent way of calculating the specific impulse in seconds is also frequently used. In this sense, specific impulse is defined as the thrust integrated over time per unit weightonEarth of the propellant:^{[2]}
where
I_{sp} is the specific impulse measured in seconds
is the average exhaust speed along the axis of the engine in (ft/s or m/s)
g_{0} is the acceleration at the Earth's surface (in ft/s^{2} or m/s^{2})
In rockets, due to atmospheric effects, the specific impulse varies with altitude, reaching a maximum in a vacuum. It is therefore most common to see the specific impulse quoted for the vehicle in a vacuum; the lower sea level values are usually indicated in some way (e.g. 'sl').^{[citation needed]}
Because of the geocentric factor of g_{0} in the equation for specific impulse, many prefer to define the specific impulse of a rocket (in particular) in terms of thrust per unit mass flow of propellant (instead of per unit weight flow). 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}. The two definitions of specific impulse are proportional to one another, and related to each other by:
where
This equation is also valid for airbreathing 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 might logically be used for specific impulse in units of N•s/kg, to avoid confusion it is desirable to reserve this for specific impulse measured in seconds.)
It is related to the thrust, or forward force on the rocket by the equation:
where
A rocket must carry all its fuel with it, so the mass of the unburned fuel must be accelerated along with the rocket itself. Minimizing the mass of fuel required to achieve a given push 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 fuel, the total change in velocity it can accomplish is proportional to the effective exhaust velocity.
A spacecraft without propulsion follows an orbit determined by the gravitational field. Deviations from the corresponding velocity pattern (these are called Δv) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.
Note that effective exhaust velocity and actual exhaust velocity can be significantly different, for example when a rocket is run within the atmosphere, atmospheric pressure on the outside of the engine causes a retarding force that reduces the specific impulse and the effective exhaust velocity goes down, whereas the actual exhaust velocity is largely unaffected. Also, sometimes rocket engines have a separate nozzle for the turbopump turbine gas, and then calculating the effective exhaust velocity requires averaging the two mass flows as well as accounting for any atmospheric pressure.^{[citation needed]}
For airbreathing jet engines, particularly turbofans, the actual exhaust velocity and the effective exhaust velocity are different by orders of magnitude. This is because a good deal of additional momentum is obtained by using air as reaction mass. This allows for a better match between the airspeed and the exhaust speed which saves energy/propellant and enormously increases the effective exhaust velocity while reducing the actual exhaust velocity.^{[citation needed]}
For rockets and rocketlike engines such as iondrives a higher implies lower energy efficiency: the power needed to run the engine is simply:
where V_{e} is the actual jet velocity.
whereas from momentum considerations the thrust generated is:
Dividing the power by the thrust to obtain the specific power requirements we get:
Hence the power needed is proportional to the exhaust velocity, with higher velocities needing higher power for the same thrust, causing less energy efficiency per unit thrust.
However, the total energy for a mission depends on total propellant use, as well as how much energy is needed per unit of propellant. For low exhaust velocity with respect to the mission deltav, enormous amounts of reaction mass is needed. In fact a very low exhaust velocity is not energy efficient at all for this reason; but it turns out that neither are very high exhaust velocities.
Theoretically, for a given deltav, in space, among all fixed values for the exhaust speed the value is the most energy efficient for a specified (fixed) final mass, see Tsiolkovsky rocket equation.
However, a variable exhaust speed can be more energy efficient still. For example, if a rocket is accelerated from some positive initial speed using an exhaust speed equal to the speed of the rocket no energy is lost as kinetic energy of reaction mass, since it becomes stationary.^{[10]} (Theoretically, by making this initial speed low and using another method of obtaining this small speed, the energy efficiency approaches 100%, but requires a large initial mass.) In this case the rocket keeps the same momentum, so its speed is inversely proportional to its remaining mass. During such a flight the kinetic energy of the rocket is proportional to its speed and, correspondingly, inversely proportional to its remaining mass. The power needed per unit acceleration is constant throughout the flight; the reaction mass to be expelled per unit time to produce a given acceleration is proportional to the square of the rocket's remaining mass.
Also it is advantageous to expel reaction mass at a location where the gravity potential is low, see Oberth effect.
Airbreathing engines such as turbojets increase the momentum generated from their propellant by using it to power the acceleration of inert air rearwards. It turns out that the amount of energy needed to generate a particular amount of thrust is inversely proportional to the amount of air propelled rearwards, thus increasing the mass of air (as with a turbofan) both improves energy efficiency as well as .
Engine  Effective exhaust velocity (m/s, kg·m/s/kg) 
Specific impulse (s) 
Energy per kg of exhaust (MJ/kg) 

Turbofan jet engine (actual V is ~300) 
29,000  3,000  ~0.05 
Solid rocket 
2,500  250  3 
Bipropellant liquid rocket 
4,400  450  9.7 
Ion thruster  29,000  3,000  430 
Dual Stage Four Grid Electrostatic Ion Thruster^{[11]}  210,000  21,400  22,500 
VASIMR^{[12]}^{[13]}^{[14]}  30,000120,000  3,00012,000  1,400 
An example of a specific impulse measured in time is 453 seconds, which is equivalent to an effective exhaust velocity of 4,440 m/s, for the Space Shuttle Main Engines when operating in a vacuum.^{[15]} An airbreathing jet engine typically has 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 around 200–400 seconds.^{[16]}
An airbreathing engine is thus much more propellant efficient than a rocket engine, because the actual exhaust speed is much lower, the air provides an oxidizer, and air is used as reaction mass. Since the physical exhaust velocity is lower, the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust (at subsonic speeds).^{[17]} While the actual exhaust velocity is lower for airbreathing engines, the effective exhaust velocity is very high for jet engines. This is because the effective exhaust velocity calculation essentially assumes that the propellant is providing all the thrust, and hence is not physically meaningful for airbreathing engines; nevertheless, it is useful for comparison with other types of engines.^{[18]}
The highest specific impulse for a chemical propellant ever testfired in a rocket engine was 542 seconds (5,320 m/s) with a tripropellant of lithium, fluorine, and hydrogen. However, this combination is impractical; see rocket fuel.^{[19]}
Nuclear thermal rocket engines differ from conventional rocket engines in that thrust is created strictly through thermodynamic phenomena, with no chemical reaction.^{[20]} The nuclear rocket typically operates by passing hydrogen gas through a superheated nuclear core. Testing in the 1960s yielded specific impulses of about 850 seconds (8,340 m/s), about twice that of the Space Shuttle engines.
A variety of other nonrocket propulsion methods, such as ion thrusters, give much higher specific impulse but with much lower thrust; for example the Hall effect thruster on the SMART1 satellite has a specific impulse of 1,640 s (16,100 m/s) but a maximum thrust of only 68 millinewtons.^{[21]} The Variable specific impulse magnetoplasma rocket (VASIMR) engine currently in development will theoretically yield 10,000−300,000 m/s but will require a large electricity source and a great deal of heavy machinery to confine even relatively diffuse plasmas, and so will be unusable for highthrust applications such as launch from planetary surfaces.^{[22]}
Here are some example numbers for larger jet and rocket engines:
Engine type  Scenario  SFC in lb/(lbf·h)  SFC in g/(kN·s)  Specific impulse (s)  Effective exhaust velocity (m/s) 

NK33 rocket engine  Vacuum  10.9  309  331^{[23]}  3,240 
SSME rocket engine  Space shuttle vacuum  7.95  225  453^{[24]}  4,423 
Ramjet  Mach 1  4.5  127  800  7,877 
J58 turbojet  SR71 at Mach 3.2 (Wet)  1.9  53.8  1,900  18,587 
RollsRoyce/Snecma Olympus 593  Concorde Mach 2 cruise (Dry)  1.195^{[25]}  33.8  3,012  29,553 
CF680C2B1F turbofan  Boeing 747400 cruise  0.605^{[25]}  17.1  5,950  58,400 
General Electric CF6 turbofan  Sea level  0.307^{[25]}  8.696  11,700  115,000 
Specific impulse is also used to measure performance in model rocket motors. Following are some of Estes' claimed values for specific impulses for several of their rocket motors:^{[26]} Estes Industries is a large, wellknown American seller of model rocket components. The specific impulse for these model rocket motors is much lower than for many other rocket motors because the manufacturer uses black powder propellant and emphasizes safety rather than maximum performance. The burn rate and hence chamber pressure and maximum thrust of model rocket motors is also tightly controlled.
Engine  Total Impulse (Ns)  Fuel Weight (N)  Specific Impulse (s) 

Estes A103T  2.5  .0370  67.49 
Estes A83  2.5  .0306  81.76 
Estes B42  5.0  .0816  61.25 
Estes B64  5.0  .0612  81.76 
Estes C63  10  .1223  81.76 
Estes C115  10  .1078  92.76 
Estes D123  20  .2443  81.86 
Estes E96  30  .3508  85.51 
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