Specific impulse
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The specific impulse (commonly abbreviated Isp) of a propulsion system is the impulse (change in momentum) per unit mass of propellant. It is used as a measure of the efficiency of the propulsion system. In practice, the specific impulses of real engines vary somewhat with both altitude and thrust; nevertheless, Isp is a useful value to compare engines; much like "miles per gallon" is used for cars.
Depending on whether the amount of propellant is expressed in mass or by weight (conventionally sea level weight on the Earth) the dimensions of specific impulse is either that of impulse per unit mass, or time, respectively, differing by a factor of g, the gravitational acceleration at the surface of the Earth.
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[edit] General considerations
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 many 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 most cases, propulsion systems with very high specific impulses (such as ion thrusters: 3000 seconds) produce low thrusts.
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.
[edit] Examples
Specific impulse of various propulsion technologies
| Engine | "Ve" eff. exhaust velocity (m/s) (= N·s/kg) |
Specific impulse (s) |
Energy per kg (MJ/kg) |
|---|---|---|---|
| Jet engine |
29,000 (actual is ~300) | 3000 | 43 |
| Solid rocket |
2500 | 250 | 3.0 |
| Bipropellant liquid rocket |
4400 | 450 | 9.7 |
| Ion thruster | 29 000 | 3000 | 430 |
| VASIMR | 290 000 | 30 000 | 43 000 |
An example of a specific impulse measured in time is 453 seconds, or, equivalently, an effective exhaust velocity of 4500 m/s, for the Space Shuttle Main Engines when operating in vacuum.
An air-breathing engine typically has a much larger specific impulse than a rocket: a jet engine may have a specific impulse of 2000−3000 seconds or more at sea level. Note also that it is more efficient; mainly due to the actual exhaust speed being lower, particularly for turbofan jets, and thus the jet engine uses far less energy to generate thrust.
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 (5320 m/s). However, this combination is impractical, see rocket fuel.
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 over a superheated nuclear core. Testing in the 1960s yielded specific impulses of about 850 seconds (8340 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 1640 s (16 100 m/s) but a maximum thrust of only 68 millinewtons. The hypothetical Variable specific impulse magnetoplasma rocket (VASIMR) propulsion should yield a minimum of 10 000−300 000 m/s but will probably require a great deal of heavy machinery to confine even relatively diffuse plasmas, so they will be unusable for very-high-thrust applications such as launch from planetary surfaces.
[edit] Units
| Specific Impulse (by weight) |
Specific Impulse (by mass) |
Effective exhaust velocity |
|
|---|---|---|---|
| SI | =1 second | =9.8 N·s/kg | =9.8 m/s |
| English units | =1 second | =1 lbf·s/lb | =32.16 ft/s |
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 nevertherless.
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 are moving towards using SI units wherever possible.
The lbf·s/lb unit sees little use but is covered in some textbooks.
[edit] Specific impulse in seconds
For all vehicles specific impulse (impulse per unit weight-on-Earth of propellant) in seconds can be defined by the following equation[1]:
where:
- Fthrust is the thrust obtained from the engine, in newtons (or poundals).
- Isp is the specific impulse measured in seconds.
is the mass flow rate in kg/s (lb/s), which is minus the time-rate of change of the vehicle's mass (weight), since propellant is being expelled.- g0 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).
[edit] Rocketry - specific impulse in seconds
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
ve 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').
[edit] Rocketry - 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 terms of thrust per unit mass flow of propellant (instead of per unit weight flow). This is an equally valid (and 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, ve. The two definitions of specific impulse are proportional to one another, and related to each other by:
where
Isp is the specific impulse in seconds
ve is the specific impulse measured in metres per second , which is the same as the effective exhaust velocity measured in metres per second (former usage in the U.S. was feet/second, though that is now obsolete)
g0 is the Earth's gravitational constant, 9.81 metres per second per second (in English units 32.2 ft/s²).
(Note that different symbols are sometimes used; for example, c is also sometimes seen for exhaust velocity. While the symbol Isp 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 mass flow rate, which is minus the time-rate of change of the vehicle's mass, since propellant is being expelled.
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.
[edit] References
- ^ Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz
