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[[File:EstesA10PT.jpg|500px|right|A figure incorporating a thrust curve for the Estes A10-PT rocket motor, as well as information about the impulse, fuel mass, and specific impulse.]]
Black Powder Rocket Motors


'''Specific impulse''' (usually abbreviated ''I''<sub>sp</sub>) is a way to describe the efficiency of [[rocket engine|rocket]] and [[jet engine|jet]] engines. It represents the [[Impulse (physics)|impulse]] (change in momentum) per unit amount of [[propellant]] used.<ref name="QRG1">{{cite web|url=http://www.qrg.northwestern.edu/projects/vss/docs/propulsion/3-what-is-specific-impulse.html|title=What is specific impulse?|publisher=Qualitative Reasoning Group|accessdate=22 December 2009}}</ref> The unit amount may be given either per unit mass (such as kilograms), or per unit Earth-weight (such as [[kilopond]]s, since '''[[standard gravity|g]]''' is used for the latter definition).<ref name="SINasa">{{cite web|url=http://www.grc.nasa.gov/WWW/K-12/airplane/specimp.html|title=Specific impulse|last=Benson|first=Tom|date=11 July 2008|publisher=NASA|accessdate=22 December 2009}}</ref> The higher the specific impulse, the less propellant is needed to gain a given amount of momentum.
==Lede==
Black powder rocket motors are used to propel model rockets and made using black powder. Black powders consist of charcoal, sulphur, and potassium nitrate, and some use dextrin as a binder. Adjustments can be made to the amount of each component to change the rate at which the black powder burns.


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.
Black powder rocket motors were created in a primitive form by the Chinese in the early 13th century, and through the years refinements have been made and several uses created. They have been used for weapons and surveillance devices as well as recreation.


Specific impulse is a useful value to compare engines, much like ''miles per gallon'' or ''litres per 100 kilometres'' is used for cars. A propulsion method with a higher specific impulse is more propellant-efficient.<ref name="QRG1" /> Another number that measures the same thing, usually used for air-breathing jet engines, is [[Thrust specific fuel consumption|specific fuel consumption]]. Specific fuel consumption is inversely proportional to specific impulse and effective exhaust velocity.
Black powder rocket motors are only produced in small sizes, to reduce the risk of explosion and a loss of efficiency. Black powder rockets are produced in classes 1/4 A through E. In larger sizes of model rocket motors, composite fuels are used that contain ammonium perchlorate or ammonium nitrate.


==General considerations==
==History==
Propellant is normally measured either in units of mass, or in units of weight at sea level on [[Earth]]. 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 metres 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 ''[[standard gravity|g]]'', the dimensioned [[Physical constant|constant]] of [[standard gravity|gravitational acceleration]] at the surface of the Earth.
Black powder is the oldest composite propellant. Its use in rockets actually preceded its use in guns.<ref name=Astro> Bedard, Andre. ‘Black Powder Rockets’. Encyclopedia Astronautica. http://www.astronautix.com/</ref> The three main components of black powder are charcoal, sulphur, and saltpeter (or potassium nitrate). It is known that by 1045, the Chinese were producing black powder, because many references to the subject were found in The Wu-ching Tsung-yao (Complete Compendium of Military Classics).<ref name=Nichro>[http://www.nichropulse.com/index.php?option=com_content&id=93&Itemid=115 Nichropulse Rocketry]</ref> In the early thirteenth century the Chinese turned black powder propelled objects, formerly only used for entertainment, into weapons of war. The first recorded use of rockets as military weapons was in 1232.<ref name=Astro /> The Chinese ‘arrows of fire’ were fired from a sort of catapult launcher. The black powder was packed in a closed tube that had a hole in one end for escaping hot gases, and a long stick as an elementary stability and guidance system.


Essentially, the higher the specific impulse, the less propellant is needed to gain a given amount of momentum. In this regard a propulsion method is more propellant-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.
Black powder had a very low specific impulse, however. Refinements in rocket design were made over the next few hundred years, at least on paper. In 1591 a Belgian, Jean Beavie, described and sketched the important idea of multistage rockets. Multistaging, placing two or more pockets of fuel in line and firing them in step fashion, is the practical answer to the problem of escaping earth's gravitational attraction.


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 thruster]]s reach 10,000 seconds—produce low thrusts.<ref name="exploreMarsnow">{{cite web|url=http://www.exploremarsnow.org/MissionOverview.html|title=Mission Overview|publisher=exploreMarsnow|accessdate=23 December 2009}}</ref>
By 1600, rockets were being used in various parts of Europe against cavalry. By 1688, rockets weighing over 120 pounds had been built and fired with success in Germany. These German rockets, carrying 16-pound warheads, used wooden powder cases reinforced with linen.


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 air-breathing engines only the mass of the fuel is counted, not the mass of air passing through the engine.
Toward the end of the eighteenth century a London lawyer, Sir William Congreve, became fascinated by the challenge of improving rockets.<ref name=pyroguide> [www.pyroguide.com/index.php?title=Black_powder_rocket PyroGuide</ref> He made extensive experimentation with propellants and case design. His systematic approach to the problem resulted in improved range, guidance (stabilization), and incendiary capabilities. The British armed forces used Congreve's new rockets to great advantage during the Napoleonic Wars.


==Examples==
In 1939 researchers at the California Institute of Technology in California, seeking to develop a high performance solid rocket motor to assist aircraft take-off, combined black powder with common road asphalt to produce the first true composite motor. This was the birth of the true composite motor and marked the end of the use of black powder in major rocketry applications.<ref name=Astro/>
{{Specific impulse examples}}
:''For a more complete list see: [[Spacecraft propulsion#Table of methods]]''


An example of a specific impulse measured in time is 453 [[second]]s, or, equivalently, an [[effective exhaust velocity]] of 4,440 [[metre per second|m/s]], for the [[Space Shuttle Main Engine]]s when operating in vacuum.
==Formulations==
Black powder rocket propellant is very similar in make-up to old fashioned gun powder. The main difference is the presence of a binder, usually dextrin. The commonly used Estes model rocket engines are made with black powder propellant.<ref name=Nichro/> Black powder propellant must be pressed very tightly in order to function well. Motors designed with black powder are most often end-burners, due to the fast burn rate of this propellant. A simple dextrin-free version (the most commonly used formulation) incorporates 75% potassium nitrate, 10% sulfur, and 15% charcoal.<ref name=pyroguide/> Dextrin may be added as desired (usually between 0 and 5%).


An air-breathing jet engine typically has a much larger specific impulse than a rocket: 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. An air-breathing engine is thus much more propellant efficient; this is because the actual exhaust speed is much lower, because air provides oxidizer, and because air is used as reaction mass. Since the actual, physical exhaust velocity is lower, for at least subsonic speeds the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust. This is so even allowing for the fact that ''more'' air must be exhausted at lower speeds to get the same thrust as a smaller amount of air at higher speeds.
==How To Make Your Own Black Powder Rocket Motor==
The method described here to create a black powder rocket motor is quite simple and requires little tooling. This describes the construction of a 12mm rocket using standard black powder as propellant; however, the same method can be scaled up or down as required.


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 essentially assumes that the propellant is providing all the thrust, and hence is not physically meaningful for air-breathing engines; nevertheless it is useful for comparison with other types of engines.
===Casing===
A variety of materials may be used for the casing, such as an aluminum, steel, or cardboard tube. The tubes should be sturdy enough to allow ramming (packing of the propellant) without damage and to withstand the internal pressure during flight.


In some ways, comparing specific impulse seems unfair in the case of jet engines and rockets. However, in rocket- or jet-powered aircraft, specific impulse is approximately proportional to range, and suborbital rockets do indeed perform much worse than jets in that regard.<!--- note that this is true even with cooptimisation- each is allowed to fly their optimum trajectory, rockets wouldn't be forced to fly through the draggy air, and jet engines wouldn't be forced to work in space! Aircraft that can do around the world circuits on a single tank of fuel have better mass fractions than orbital rockets, so I've removed the altitude constraint.--->
===Propellant===
Simple black powder in the standard ratio (75:15:10) works well to propel the rocket, and several additives may be added to different effects. For example, additional (coarse) charcoal or metal powders (5 - 10%) may be added to obtain an interesting spark trail. However, this may alter the burn rate of the mixture slightly, perhaps requiring you to adjust the dimensions of the nozzle.<ref name=Astro/>


The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was lithium, fluorine, and hydrogen (a [[Tripropellant rocket|tripropellant]]): 542 seconds (5,320&nbsp;m/s). However, this combination is impractical; see [[rocket fuel]].<ref>ARBIT, H. A., CLAPP, S. D., DICKERSON, R. A., NAGAI, C. K., [http://www.aiaa.org/content.cfm?pageid=406&gTable=mtgpaper&gID=40999 Combustion characteristics of the fluorine-lithium/hydrogen tripropellant combination.] AMERICAN INST OF AERONAUTICS AND ASTRONAUTICS, PROPULSION JOINT SPECIALIST CONFERENCE, 4TH, CLEVELAND, OHIO, Jun 10-14, 1968.</ref>
===The Nozzle===
Black powder rockets require a nozzle. This is a plug in the exhaust end of the rocket that has a small opening. The nozzle allows the gases produced by the black powder to build up more pressure. This increases the exhaust velocity, and therefore thrust. The dimensions of the nozzle are critical to rocket performance. Ideally, the nozzle will be small enough to allow the internal pressure to rise, yet not so small as to allow the pressure to rise to a point that the rocket explodes.<ref name=sky>[http://www.skylighter.com/fireworks/How-to-make-sky-rockets/black-powder-rockets.asp Skylighter Pyrotechnics</ref>


[[Nuclear thermal rocket]] engines differ from conventional rocket engines in that thrust is created strictly through thermodynamic phenomena, with no chemical reaction. The nuclear rocket typically operates by passing hydrogen gas through a superheated nuclear core. [http://www.lascruces.com/~mrpbar/rocket.html Testing in the 1960s] yielded specific impulses of about 850 seconds (8,340&nbsp;m/s), about twice that of the Space Shuttle engines.
Nozzles for fireworks rockets are usually made with clay. Bentonite and kaolin clay work well. If necessary, a small amount of fine sand may be added to improve the nozzle's grip on the casing. The dry clay powder is rammed into the casing, producing a solid plug. This powder can be used to produce rock-hard nozzles that erode very little.


A variety of other non-rocket propulsion methods, such as [[ion thruster]]s, 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 (16,100&nbsp;m/s) but a maximum thrust of only 68 millinewtons. The hypothetical [[Variable specific impulse magnetoplasma rocket]] (VASIMR) propulsion would theoretically yield a minimum of 10,000−300,000&nbsp;m/s but would probably require a great deal of heavy machinery to confine even relatively diffuse plasmas, and so would be unusable for high-thrust applications such as launch from planetary surfaces.
Another nozzle material that is quite resistant to erosion is quick-hardening cement. It is wetted with water and pressed into the casing. After a few minutes it has solidified enough to continue with the construction of the motor. Disadvantages are that it is very sticky when wet (making working with it very messy), and the short hardening time which makes it necessary to work quickly.


The proposed [[Project Orion (nuclear propulsion)|Project Orion]] nuclear propelled spaceship provided a specific impulse of 10,000—1,000,000 s.<ref>[http://www.daviddarling.info/encyclopedia/O/OrionProj.html Project Orion entry in the Internet Encyclopedia of Science:]</ref>
Less resistant to erosion are plaster of paris and polyester. These are not ideal but they may be used for low temperature propellants, such as 'five cent sugar rocket' propellant.


==Performance==
==Units==
[[Image:Model Rocket Motors.jpg|thumb|200px| The four leftmost motors are Estes black powder rocket motors.]]

The impulse (area under the thrust-time curve) of a black powder motor is used to determine its class. Motors are divided into classes from 1/4A to E, which covers an impulse range of 0 to 40 Ns (Newtons*seconds). Other types of model rocket motors can be classified up to an ‘H’, which is up to 320 Ns, and even further in some cases. Each classes upper limit is double the upper limit of the previous classes.


{| class="wikitable"
{| class="wikitable"
|
!align="right"|'''Specific Impulse<br>(by weight)'''<br>
!align="right"|'''Specific Impulse<br>(by mass)'''<br>
!align="right"|'''Effective exhaust velocity'''<br>
!align="right"|'''Specific fuel consumption'''<br>
|-
|-
!'''SI'''
! rowspan="1"|Class || colspan="1"|Total Impulse (Ns)
|=X seconds
|-----
|=9.8066 X N·s/kg
| 1/4A || align="left" | 0.001 – 0.625
|=9.8066 X m/s
|-----
|=(101,972/X) g/kN·s
| 1/2A || align="left" | 0.626 – 1.250
|-----
|-
!'''English units'''
| A || align="left"| 1.251 – 2.500
|=X seconds
|-----
|=X lbf·s/lb
| B || align="left" | 2.501 – 5.000
|=32.16 X ft/s
|-----
|=(3,600/X) lb/lbf·h
| C || align="left" | 5.001 – 10.000
|-----
| D || align="left" | 10.001 – 20.000
|-----
| E || align="left" | 20.001 – 40.000
|}
|}


By far the most common units 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 is 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.
Figures from tests of Estes rocket motors are used in the following examples of rocket motor performance.<ref name=Apogee>http://www.apogeerockets.com/estes_items.asp</ref>


The effective exhaust velocity 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 not precisely the same as the actual exhaust speed due to, for example, fuel and oxidizer that is dumped overboard after powering turbopumps. For airbreathing engines it is not physically meaningful although can be used for comparison purposes nevertheless.
For miniature black powder rocket motors (13 mm diameter), the maximum thrust is between 5 and 12 N, the total impulse is between .5 and 2.2 Ns, and the burn time is between .25 and 1 second. For Estes ‘regular size’ rocket motors (18 mm diameter), there are three classes: A, B, and C. The A class 18 mm motors have a maximum thrust between 9.5 and 9.75 N, a total impulse between 2.1 and 2.3 Ns, and a burn time between .5 and .75 seconds. The B class 18 mm motors have a maximum thrust between 12.15 and 12.75 N, a total impulse between 4.2 and 4.35 Ns, and a burn time between .85 and 1 second. The C class 18mm motors have a maximum thrust from 14 – 14.15 N, a total impulse between 8.8 and 9 Ns, and a burn time between 1.85 and 2 seconds.


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.)
There are also 3 classes included in Estes large (24 mm diameter) rocket motors: C, D, and E. The C class 24 mm motors have a maximum thrust between 21.6 and 21.75 N, a total impulse of between 8.8 and 9 Ns, and a burn time between .8 and .85 seconds. The D class 24 mm motors have a maximum thrust between 29.7 and 29.8 N, a total impulse between 16.7 and 16.85 Ns, and a burn time between 1.6 and 1.7 seconds. The E class 24 mm motors have a maximum thrust between 19.4 and 19.5 N, a total impulse between 28.45 and 28.6 Ns, and a burn time between 3 and 3.1 seconds.


The units of ft/s were used by NASA during Apollo, but seems to have fallen into disuse, and NASA is moving towards using SI units wherever possible.{{Citation needed|date=April 2009}}
===Problems and Troubleshooting===
There are several easily fixed and diagnosed problems common to black powder rocket motors. If the rocket nozzle blows out at or shortly after ignition, then there are several possible problems: the clay was not rammed hard enough, the clay used in the nozzle was too coarse and therefore was not rammed tightly enough, or the propellant is burning too quickly. If the propellant is burning too quickly, add charcoal to slow the burn rate.<ref name=sky/>


The lbf·s/lb unit sees little use but is covered in some textbooks.{{Citation needed|date=April 2009}}
If the rocket engine blows up at or shortly after ignition, there are several possible reasons. The propellant may be burning too fast, in which case more charcoal needs to be added to reduce the burn rate. The propellant may not have been rammed tightly enough. The propellant also may contain internal cracks, from rough handling or a change in humidity.


Another equivalent unit is [[Thrust specific fuel consumption|specific fuel consumption]]. This has units of g/kN.s or lbf/lb·h and is inversely proportional to specific impulse. This is used extensively for describing air-breathing jet engines.
If the rocket takes off but acceleration is sluggish, then the propellant may be burning too slowly, and more potassium nitrate must be added. If this is the case, also make sure that the rocket is being lit correctly.

==Specific impulse in seconds==
===General definition===
For all vehicles specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the following equation<ref>Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz</ref>:

:<math>\mathrm{F_{\rm thrust}}=I_{\rm sp} \cdot \frac{\Delta m} {\Delta t} \cdot g_{\rm 0} \,</math>

where:

:<math>\mathrm{F_{\rm thrust}}</math> is the thrust obtained from the engine, in [[newton (unit)|newton]]s (or [[poundal]]s).
:<math>I_{\rm sp}</math> is the specific impulse measured in seconds.
:'''<math>\frac {\Delta m} {\Delta t} </math>''' is the [[mass flow rate]] in kg/s (lb/s), which is negative the time-rate of change of the vehicle's mass since propellant is being expelled.
:<math>g_{\rm 0}</math> is the acceleration at the Earth's surface, in m/s² (or ft/s²).

(When working with [[English unit]]s, it is conventional to divide both sides of the equation by ''g''<sub>0</sub> so that the left hand side of the equation has units of lbs rather than expressing it in [[poundal]]s.)

This ''I<sub>sp</sub>'' in seconds value is somewhat physically meaningful&mdash;if an engine's thrust could be adjusted to equal the initial weight of its propellant (measured at one [[standard gravity]]), then ''I''<sub>sp</sub> is the duration the propellant would last.

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).

[[Image:Specific-impulse-kk-20090105.png|thumb|center|700px|The specific impulse of various jet engines]]

===Rocketry===

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 change in momentum per unit [[weight]]-on-Earth of the propellant:

:<math>I_{\rm sp}=\frac{v_{\rm e}}{g_{\rm 0}}</math>

where

''I''<sub>sp</sub> is the specific impulse measured in seconds

<math>v_{\rm e}</math> is the average exhaust speed along the axis of the engine in (ft/s or m/s)

''g<sub>0</sub>'' is the acceleration at the Earth's surface (in ft/s<sup>2</sup> or m/s<sup>2</sup>)

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').

==Specific impulse as a speed (effective exhaust velocity)==
Because of the geocentric factor of ''g''<sub>0</sub> 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<sub>e</sub>. The two definitions of specific impulse are proportional to one another, and related to each other by:

:<math>v_{\rm e} = g_0 I_{\rm sp} \,</math>

where

:<math>I_{\rm sp} \,</math> - is the specific impulse in seconds

:<math>v_{\rm e} \,</math> - is the specific impulse measured in [[metre per second|m/s]], which is the same as the effective exhaust velocity measured in m/s (or ft/s if g is in ft/s<sup>2</sup>)

:<math>g_0 \,</math> - is the acceleration due to gravity at the Earth's surface, 9.81 m/s² (in [[English units]] units 32.2 ft/s²).

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 <math>I_{sp}</math> 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:

:<math>\mathrm{F_{\rm thrust}}=v_{\rm e} \cdot \frac {\Delta m} {\Delta t} \,</math>

where

<math>\frac {\Delta m} {\Delta t} </math> is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass

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. Using [[Newton's laws of motion]] it is not difficult to verify that for a fixed mass of fuel, the total change in [[velocity]] (in fact, momentum) it can accomplish can only be increased by increasing 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 [[delta v|Δ''v'']]) are achieved by sending exhaust mass in the direction opposite to that of the desired velocity change.

===Actual exhaust speed versus effective exhaust speed===

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.

For airbreathing jet engines, particularly, [[turbofan]]s, 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.

==Energy efficiency==
===Rockets===
For rockets and rocket-like engines such as ion-drives a higher <math>I_{sp}</math> implies lower energy efficiency: the power needed to run the engine is simply:

:<math>\frac {dm} {dt} \frac { V_e^2 } {2}</math>

where V<sub>e</sub> is the actual jet velocity.

whereas from momentum considerations the thrust generated is:

:<math>\frac {dm} {dt} V_e</math>

Dividing the power by the thrust to obtain the specific power requirements we get:

:<math>\frac {V_e} {2}</math>

Hence the power needed is proportional to the exhaust velocity, with higher velocities needing higher power for the same thrust, and thus are less energy efficient 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 delta-v, 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 [[delta-v]], in space, among all fixed values for the exhaust speed the value <math>v_\text{e}=0.6275 \Delta v</math> is the most energy efficient with respect to the 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.<ref>Note that this limits the speed of the rocket to the maximum exhaust speed.</ref> 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]].

===Air breathing===
Air-breathing engines such as [[turbojet]]s 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 <math>I_{sp}</math>.

==Figures for real engines==
{{Thrust engine efficiency}}


==References==
==References==
{{Reflist}}
{{Reflist}}
{{Refbegin}}
{{Refend}}

==External links==
*[http://software.lpre.de/ RPA - Design Tool for Liquid Rocket Engine Analysis]
*[http://www.braeunig.us/space/propel.htm List of Specific Impulses of various rocket fuels]

==See also==
<div style="-moz-column-count:2; column-count:2;">
*[[Jet engine]]
*[[Impulse (physics)|Impulse]] - the change in momentum
*[[Tsiolkovsky rocket equation]]
*[[System-specific impulse]]
*[[Specific energy]]
*[[Thrust specific fuel consumption]] - fuel consumption per unit thrust
*[[Specific thrust]] thrust per unit of air for a duct engine
*[[Heating value]]
*[[Energy density]]
*[[Delta-v (physics)]]

</div>

{{DEFAULTSORT:Specific Impulse}}
<!--Categories-->
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Revision as of 22:08, 3 July 2011

A figure incorporating a thrust curve for the Estes A10-PT rocket motor, as well as information about the impulse, fuel mass, and specific impulse.
A figure incorporating a thrust curve for the Estes A10-PT rocket motor, as well as information about the impulse, fuel mass, and specific impulse.

Specific impulse (usually abbreviated Isp) is a way to describe the efficiency of rocket and jet engines. It represents the impulse (change in momentum) per unit amount of propellant used.[1] The unit amount may be given either per unit mass (such as kilograms), or per unit Earth-weight (such as kiloponds, since g is used for the latter definition).[2] The higher the specific impulse, the less propellant is needed to gain a given amount of momentum.

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. A propulsion method with a higher specific impulse is more propellant-efficient.[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.

General considerations

Propellant is normally measured either in units of mass, or in units of weight at sea level on Earth. 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 metres 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.

Essentially, the higher the specific impulse, the less propellant is needed to gain a given amount of momentum. In this regard a propulsion method is more propellant-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.

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.[3]

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 air-breathing engines only the mass of the fuel is counted, not the mass of air passing through the engine.

Examples

Specific impulse of various propulsion technologies
Engine Effective exhaust velocity (m/s) Specific impulse (s) Exhaust specific energy (MJ/kg)
Turbofan jet engine (actual V is ~300 m/s) 29,000 3,000 Approx. 0.05
Space Shuttle Solid Rocket Booster 2,500 250 3
Liquid oxygenliquid hydrogen 4,400 450 9.7
NSTAR[4] electrostatic xenon ion thruster 20,000–30,000 1,950–3,100
NEXT electrostatic xenon ion thruster 40,000 1,320–4,170
VASIMR predictions[5][6][7] 30,000–120,000 3,000–12,000 1,400
DS4G electrostatic ion thruster[8] 210,000 21,400 22,500
Ideal photonic rocket[a] 299,792,458 30,570,000 89,875,517,874
For a more complete list see: Spacecraft propulsion#Table of methods

An example of a specific impulse measured in time is 453 seconds, or, equivalently, an effective exhaust velocity of 4,440 m/s, for the Space Shuttle Main Engines when operating in vacuum.

An air-breathing jet engine typically has a much larger specific impulse than a rocket: 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. An air-breathing engine is thus much more propellant efficient; this is because the actual exhaust speed is much lower, because air provides oxidizer, and because air is used as reaction mass. Since the actual, physical exhaust velocity is lower, for at least subsonic speeds the kinetic energy the exhaust carries away is lower and thus the jet engine uses far less energy to generate thrust. This is so even allowing for the fact that more air must be exhausted at lower speeds to get the same thrust as a smaller amount of air at higher speeds.

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 essentially assumes that the propellant is providing all the thrust, and hence is not physically meaningful for air-breathing engines; nevertheless it is useful for comparison with other types of engines.

In some ways, comparing specific impulse seems unfair in the case of jet engines and rockets. However, in rocket- or jet-powered aircraft, specific impulse is approximately proportional to range, and suborbital rockets do indeed perform much worse than jets in that regard.

The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was lithium, fluorine, and hydrogen (a tripropellant): 542 seconds (5,320 m/s). However, this combination is impractical; see rocket fuel.[9]

Nuclear thermal rocket engines differ from conventional rocket engines in that thrust is created strictly through thermodynamic phenomena, with no chemical reaction. 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 non-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 (16,100 m/s) but a maximum thrust of only 68 millinewtons. The hypothetical Variable specific impulse magnetoplasma rocket (VASIMR) propulsion would theoretically yield a minimum of 10,000−300,000 m/s but would probably require a great deal of heavy machinery to confine even relatively diffuse plasmas, and so would be unusable for high-thrust applications such as launch from planetary surfaces.

The proposed Project Orion nuclear propelled spaceship provided a specific impulse of 10,000—1,000,000 s.[10]

Units

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
English units =X seconds =X lbf·s/lb =32.16 X ft/s =(3,600/X) lb/lbf·h

By far the most common units 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 is 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.

The effective exhaust velocity 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 not precisely the same as the actual exhaust speed due to, for example, fuel and oxidizer that is dumped overboard after powering turbopumps. For airbreathing engines it is not physically meaningful although can be used for comparison purposes nevertheless.

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.)

The units of ft/s were used by NASA during Apollo, but seems to have fallen into disuse, and NASA is moving towards using SI units wherever possible.[citation needed]

The lbf·s/lb unit sees little use but is covered in some textbooks.[citation needed]

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. This is used extensively for describing air-breathing jet engines.

Specific impulse in seconds

General definition

For all vehicles specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the following equation[11]:

where:

is the thrust obtained from the engine, in newtons (or poundals).
is the specific impulse measured in seconds.
is the mass flow rate in kg/s (lb/s), which is negative the time-rate of change of the vehicle's mass since propellant is being expelled.
is the acceleration at the Earth's surface, in m/s² (or ft/s²).

(When working with English units, it is conventional to divide both sides of the equation by g0 so that the left hand side of the equation has units of lbs rather than expressing it in poundals.)

This Isp 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 Isp is the duration the propellant would last.

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).

The specific impulse of various jet engines

Rocketry

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 change in momentum per unit weight-on-Earth of the propellant:

where

Isp is the specific impulse measured in seconds

is the average exhaust speed along the axis of the engine in (ft/s or m/s)

g0 is the acceleration at the Earth's surface (in ft/s2 or m/s2)

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').

Specific impulse as a speed (effective exhaust velocity)

Because of the geocentric factor of g0 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, ve. The two definitions of specific impulse are proportional to one another, and related to each other by:

where

- is the specific impulse in seconds
- is the specific impulse measured in m/s, which is the same as the effective exhaust velocity measured in m/s (or ft/s if g is in ft/s2)
- is the acceleration due to gravity at the Earth's surface, 9.81 m/s² (in English units units 32.2 ft/s²).

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

is the propellant mass flow rate, which is the rate of decrease of the vehicle's mass

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. Using Newton's laws of motion it is not difficult to verify that for a fixed mass of fuel, the total change in velocity (in fact, momentum) it can accomplish can only be increased by increasing 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.

Actual exhaust speed versus effective exhaust speed

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.

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.

Energy efficiency

Rockets

For rockets and rocket-like engines such as ion-drives a higher implies lower energy efficiency: the power needed to run the engine is simply:

where Ve 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, and thus are less energy efficient 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 delta-v, 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 delta-v, in space, among all fixed values for the exhaust speed the value is the most energy efficient with respect to the 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.[12] 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.

Air breathing

Air-breathing 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 .

Figures for real engines

Rocket engines in vacuum
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
Avio P80 solid fuel 2006 Vega stage 1 13 360 280 2700
Avio Zefiro 23 solid fuel 2006 Vega stage 2 12.52 354.7 287.5 2819
Avio Zefiro 9A solid fuel 2008 Vega stage 3 12.20 345.4 295.2 2895
Merlin 1D liquid fuel 2013 Falcon 9 12 330 310 3000
RD-843 liquid fuel Vega upper stage 11.41 323.2 315.5 3094
Kuznetsov NK-33 liquid fuel 1970s N-1F, Soyuz-2-1v stage 1 10.9 308 331[13] 3250
NPO Energomash RD-171M liquid fuel Zenit-2M, -3SL, -3SLB, -3F stage 1 10.7 303 337 3300
LE-7A cryogenic H-IIA, H-IIB stage 1 8.22 233 438 4300
Snecma HM-7B cryogenic Ariane 2, 3, 4, 5 ECA upper stage 8.097 229.4 444.6 4360
LE-5B-2 cryogenic H-IIA, H-IIB upper stage 8.05 228 447 4380
Aerojet Rocketdyne RS-25 cryogenic 1981 Space Shuttle, SLS stage 1 7.95 225 453[14] 4440
Aerojet Rocketdyne RL-10B-2 cryogenic Delta III, Delta IV, SLS upper stage 7.734 219.1 465.5 4565
NERVA NRX A6 nuclear 1967 869
Jet engines with Reheat, static, sea level
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
Turbo-Union RB.199 turbofan Tornado 2.5[15] 70.8 1440 14120
GE F101-GE-102 turbofan 1970s B-1B 2.46 70 1460 14400
Tumansky R-25-300 turbojet MIG-21bis 2.206[15] 62.5 1632 16000
GE J85-GE-21 turbojet F-5E/F 2.13[15] 60.3 1690 16570
GE F110-GE-132 turbofan F-16E/F 2.09[15] 59.2 1722 16890
Honeywell/ITEC F125 turbofan F-CK-1 2.06[15] 58.4 1748 17140
Snecma M53-P2 turbofan Mirage 2000C/D/N 2.05[15] 58.1 1756 17220
Snecma Atar 09C turbojet Mirage III 2.03[15] 57.5 1770 17400
Snecma Atar 09K-50 turbojet Mirage IV, 50, F1 1.991[15] 56.4 1808 17730
GE J79-GE-15 turbojet F-4E/EJ/F/G, RF-4E 1.965 55.7 1832 17970
Saturn AL-31F turbofan Su-27/P/K 1.96[16] 55.5 1837 18010
GE F110-GE-129 turbofan F-16C/D, F-15EX 1.9[15] 53.8 1895 18580
Soloviev D-30F6 turbofan MiG-31, S-37/Su-47 1.863[15] 52.8 1932 18950
Lyulka AL-21F-3 turbojet Su-17, Su-22 1.86[15] 52.7 1935 18980
Klimov RD-33 turbofan 1974 MiG-29 1.85 52.4 1946 19080
Saturn AL-41F-1S turbofan Su-35S/T-10BM 1.819 51.5 1979 19410
Volvo RM12 turbofan 1978 Gripen A/B/C/D 1.78[15] 50.4 2022 19830
GE F404-GE-402 turbofan F/A-18C/D 1.74[15] 49 2070 20300
Kuznetsov NK-32 turbofan 1980 Tu-144LL, Tu-160 1.7 48 2100 21000
Snecma M88-2 turbofan 1989 Rafale 1.663 47.11 2165 21230
Eurojet EJ200 turbofan 1991 Eurofighter 1.66–1.73 47–49[17] 2080–2170 20400–21300
Dry jet engines, static, sea level
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
GE J85-GE-21 turbojet F-5E/F 1.24[15] 35.1 2900 28500
Snecma Atar 09C turbojet Mirage III 1.01[15] 28.6 3560 35000
Snecma Atar 09K-50 turbojet Mirage IV, 50, F1 0.981[15] 27.8 3670 36000
Snecma Atar 08K-50 turbojet Super Étendard 0.971[15] 27.5 3710 36400
Tumansky R-25-300 turbojet MIG-21bis 0.961[15] 27.2 3750 36700
Lyulka AL-21F-3 turbojet Su-17, Su-22 0.86 24.4 4190 41100
GE J79-GE-15 turbojet F-4E/EJ/F/G, RF-4E 0.85 24.1 4240 41500
Snecma M53-P2 turbofan Mirage 2000C/D/N 0.85[15] 24.1 4240 41500
Volvo RM12 turbofan 1978 Gripen A/B/C/D 0.824[15] 23.3 4370 42800
RR Turbomeca Adour turbofan 1999 Jaguar retrofit 0.81 23 4400 44000
Honeywell/ITEC F124 turbofan 1979 L-159, X-45 0.81[15] 22.9 4440 43600
Honeywell/ITEC F125 turbofan F-CK-1 0.8[15] 22.7 4500 44100
PW J52-P-408 turbojet A-4M/N, TA-4KU, EA-6B 0.79 22.4 4560 44700
Saturn AL-41F-1S turbofan Su-35S/T-10BM 0.79 22.4 4560 44700
Snecma M88-2 turbofan 1989 Rafale 0.782 22.14 4600 45100
Klimov RD-33 turbofan 1974 MiG-29 0.77 21.8 4680 45800
RR Pegasus 11-61 turbofan AV-8B+ 0.76 21.5 4740 46500
Eurojet EJ200 turbofan 1991 Eurofighter 0.74–0.81 21–23[17] 4400–4900 44000–48000
GE F414-GE-400 turbofan 1993 F/A-18E/F 0.724[18] 20.5 4970 48800
Kuznetsov NK-32 turbofan 1980 Tu-144LL, Tu-160 0.72-0.73 20–21 4900–5000 48000–49000
Soloviev D-30F6 turbofan MiG-31, S-37/Su-47 0.716[15] 20.3 5030 49300
Snecma Larzac turbofan 1972 Alpha Jet 0.716 20.3 5030 49300
IHI F3 turbofan 1981 Kawasaki T-4 0.7 19.8 5140 50400
Saturn AL-31F turbofan Su-27 /P/K 0.666-0.78[16][18] 18.9–22.1 4620–5410 45300–53000
RR Spey RB.168 turbofan AMX 0.66[15] 18.7 5450 53500
GE F110-GE-129 turbofan F-16C/D, F-15 0.64[18] 18 5600 55000
GE F110-GE-132 turbofan F-16E/F 0.64[18] 18 5600 55000
Turbo-Union RB.199 turbofan Tornado ECR 0.637[15] 18.0 5650 55400
PW F119-PW-100 turbofan 1992 F-22 0.61[18] 17.3 5900 57900
Turbo-Union RB.199 turbofan Tornado 0.598[15] 16.9 6020 59000
GE F101-GE-102 turbofan 1970s B-1B 0.562 15.9 6410 62800
PW TF33-P-3 turbofan B-52H, NB-52H 0.52[15] 14.7 6920 67900
RR AE 3007H turbofan RQ-4, MQ-4C 0.39[15] 11.0 9200 91000
GE F118-GE-100 turbofan 1980s B-2 0.375[15] 10.6 9600 94000
GE F118-GE-101 turbofan 1980s U-2S 0.375[15] 10.6 9600 94000
General Electric CF6-50C2 turbofan A300, DC-10-30 0.371[15] 10.5 9700 95000
GE TF34-GE-100 turbofan A-10 0.37[15] 10.5 9700 95000
CFM CFM56-2B1 turbofan C-135, RC-135 0.36[19] 10 10000 98000
Progress D-18T turbofan 1980 An-124, An-225 0.345 9.8 10400 102000
PW F117-PW-100 turbofan C-17 0.34[20] 9.6 10600 104000
PW PW2040 turbofan Boeing 757 0.33[20] 9.3 10900 107000
CFM CFM56-3C1 turbofan 737 Classic 0.33 9.3 11000 110000
GE CF6-80C2 turbofan 744, 767, MD-11, A300/310, C-5M 0.307-0.344 8.7–9.7 10500–11700 103000–115000
EA GP7270 turbofan A380-861 0.299[18] 8.5 12000 118000
GE GE90-85B turbofan 777-200/200ER/300 0.298[18] 8.44 12080 118500
GE GE90-94B turbofan 777-200/200ER/300 0.2974[18] 8.42 12100 118700
RR Trent 970-84 turbofan 2003 A380-841 0.295[18] 8.36 12200 119700
GE GEnx-1B70 turbofan 787-8 0.2845[18] 8.06 12650 124100
RR Trent 1000C turbofan 2006 787-9 0.273[18] 7.7 13200 129000
Jet engines, cruise
Model Type First
run
Application TSFC Isp (by weight) Isp (by mass)
lb/lbf·h g/kN·s s m/s
Ramjet Mach 1 4.5 130 800 7800
J-58 turbojet 1958 SR-71 at Mach 3.2 (Reheat) 1.9[15] 53.8 1895 18580
RR/Snecma Olympus turbojet 1966 Concorde at Mach 2 1.195[21] 33.8 3010 29500
PW JT8D-9 turbofan 737 Original 0.8[22] 22.7 4500 44100
Honeywell ALF502R-5 GTF BAe 146 0.72[20] 20.4 5000 49000
Soloviev D-30KP-2 turbofan Il-76, Il-78 0.715 20.3 5030 49400
Soloviev D-30KU-154 turbofan Tu-154M 0.705 20.0 5110 50100
RR Tay RB.183 turbofan 1984 Fokker 70, Fokker 100 0.69 19.5 5220 51200
GE CF34-3 turbofan 1982 Challenger, CRJ100/200 0.69 19.5 5220 51200
GE CF34-8E turbofan E170/175 0.68 19.3 5290 51900
Honeywell TFE731-60 GTF Falcon 900 0.679[23] 19.2 5300 52000
CFM CFM56-2C1 turbofan DC-8 Super 70 0.671[20] 19.0 5370 52600
GE CF34-8C turbofan CRJ700/900/1000 0.67-0.68 19–19 5300–5400 52000–53000
CFM CFM56-3C1 turbofan 737 Classic 0.667 18.9 5400 52900
CFM CFM56-2A2 turbofan 1974 E-3, E-6 0.66[19] 18.7 5450 53500
RR BR725 turbofan 2008 G650/ER 0.657 18.6 5480 53700
CFM CFM56-2B1 turbofan C-135, RC-135 0.65[19] 18.4 5540 54300
GE CF34-10A turbofan ARJ21 0.65 18.4 5540 54300
CFE CFE738-1-1B turbofan 1990 Falcon 2000 0.645[20] 18.3 5580 54700
RR BR710 turbofan 1995 G. V/G550, Global Express 0.64 18 5600 55000
GE CF34-10E turbofan E190/195 0.64 18 5600 55000
General Electric CF6-50C2 turbofan A300B2/B4/C4/F4, DC-10-30 0.63[20] 17.8 5710 56000
PowerJet SaM146 turbofan Superjet LR 0.629 17.8 5720 56100
CFM CFM56-7B24 turbofan 737 NG 0.627[20] 17.8 5740 56300
RR BR715 turbofan 1997 717 0.62 17.6 5810 56900
GE CF6-80C2-B1F turbofan 747-400 0.605[21] 17.1 5950 58400
CFM CFM56-5A1 turbofan A320 0.596 16.9 6040 59200
Aviadvigatel PS-90A1 turbofan Il-96-400 0.595 16.9 6050 59300
PW PW2040 turbofan 757-200 0.582[20] 16.5 6190 60700
PW PW4098 turbofan 777-300 0.581[20] 16.5 6200 60800
GE CF6-80C2-B2 turbofan 767 0.576[20] 16.3 6250 61300
IAE V2525-D5 turbofan MD-90 0.574[24] 16.3 6270 61500
IAE V2533-A5 turbofan A321-231 0.574[24] 16.3 6270 61500
RR Trent 700 turbofan 1992 A330 0.562[25] 15.9 6410 62800
RR Trent 800 turbofan 1993 777-200/200ER/300 0.560[25] 15.9 6430 63000
Progress D-18T turbofan 1980 An-124, An-225 0.546 15.5 6590 64700
CFM CFM56-5B4 turbofan A320-214 0.545 15.4 6610 64800
CFM CFM56-5C2 turbofan A340-211 0.545 15.4 6610 64800
RR Trent 500 turbofan 1999 A340-500/600 0.542[25] 15.4 6640 65100
CFM LEAP-1B turbofan 2014 737 MAX 0.53-0.56 15–16 6400–6800 63000–67000
Aviadvigatel PD-14 turbofan 2014 MC-21-310 0.526 14.9 6840 67100
RR Trent 900 turbofan 2003 A380 0.522[25] 14.8 6900 67600
GE GE90-85B turbofan 777-200/200ER 0.52[20][26] 14.7 6920 67900
GE GEnx-1B76 turbofan 2006 787-10 0.512[22] 14.5 7030 69000
PW PW1400G GTF MC-21 0.51[27] 14.4 7100 69000
CFM LEAP-1C turbofan 2013 C919 0.51 14.4 7100 69000
CFM LEAP-1A turbofan 2013 A320neo family 0.51[27] 14.4 7100 69000
RR Trent 7000 turbofan 2015 A330neo 0.506[b] 14.3 7110 69800
RR Trent 1000 turbofan 2006 787 0.506[c] 14.3 7110 69800
RR Trent XWB-97 turbofan 2014 A350-1000 0.478[d] 13.5 7530 73900
PW 1127G GTF 2012 A320neo 0.463[22] 13.1 7780 76300

References

  1. ^ a b "What is specific impulse?". Qualitative Reasoning Group. Retrieved 22 December 2009.
  2. ^ Benson, Tom (11 July 2008). "Specific impulse". NASA. Retrieved 22 December 2009.
  3. ^ "Mission Overview". exploreMarsnow. Retrieved 23 December 2009.
  4. ^ In-flight performance of the NSTAR ion propulsion system on the Deep Space One mission. Aerospace Conference Proceedings. IEEExplore. 2000. doi:10.1109/AERO.2000.878373.
  5. ^ Glover, Tim W.; Chang Diaz, Franklin R.; Squire, Jared P.; Jacobsen, Verlin; Chavers, D. Gregory; Carter, Mark D. "Principal VASIMR Results and Present Objectives" (PDF).
  6. ^ Cassady, Leonard D.; Longmier, Benjamin W.; Olsen, Chris S.; Ballenger, Maxwell G.; McCaskill, Greg E.; Ilin, Andrew V.; Carter, Mark D.; Gloverk, Tim W.; Squire, Jared P.; Chang, Franklin R.; Bering, III, Edgar A. (28 July 2010). "VASIMR R Performance Results" (PDF). www.adastra.com.
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See also


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