Talk:Specific impulse/temp

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The specific impulse (commonly abbreviated Isp) of a propulsion system is the impulse produced (change in momentum of a free body) per unit of propellant expended.

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[edit] Units

There is inconsistency and ambiguity in the units of specific impulse. Specific impulse has been reported in units of lb-sec per lb,[1] lbf·s/lbm[2] and seconds.[3] These values that are not in seconds would be numerically unchanged if expressed in the units of seconds.

In United States customary units, specific impulse is often given in seconds. This requires a weight rate of propellant expended to get thrust in lbf without multiplying by g0. The propellant weight is in lbf and is the force that is required to support a mass of a lbm at standard gravity. This is what a balance scale says. Thus the force in lbf that a thrusting device produces is equal to the Isp in seconds times the weight flow rate of propellant in lbf/s.[1]

In metric (SI) units, impulse is determined per unit mass of propellant expended so the units are N·s/kg.[4] But specific impulse is often reported in seconds. Multiply the value in seconds by the standard acceleration of gravity, 9.80665 m/s², to get the effective exhaust velocity in m/s. Effective exhaust velocity in m/s is numerically the same (apply Newton’s second law to change the units) as a specific impulse based on propellant mass flow rate. Thus the thrust in newtons that a thrusting device produces is equal to the effective exhaust velocity in m/s (=N·s/kg) times the propellant mass flow rate in kg/s. The multiplication of Isp in seconds by standard gravity is included in the formula below to calculate thrust in newtons. Sometimes specific impulse is reported in units of N·s/kg which simply means that multiplication by standard gravity has already been accounted for.

[edit] Standard specific impulse

The specific impulse that a rocket delivers varies with the chamber pressure, nozzle expansion ratio, nozzle configuration, ambient pressure and the fuel that is used. To compare propellants, engines, and various other design parameters the standard specific impulse is determined for standard conditions.[5] The standard chamber pressure is 6895 kPa (1000 psia). The standard nozzle is that which results in an exit pressure of one atmosphere at sea level. Test results are corrected to sea level ambient pressure. Specific impulse numbers that are given for propellants are usually for standard conditions unless stated otherwise.

[edit] General considerations

Higher specific impulse means less propellant is needed to produce a given amount of impulse. 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.

Thrust and specific impulse should not be confused with one another. Specific impulse is a measure of the impulse per unit of propellant that is expended, while the integral of thrust times time is impulse. Thrust is a measure of the instantaneous force produced by a particular engine. In fact, propulsion systems with very high specific impulses (such as ion thrusters: 3,000 seconds) are power limited to producing low thrusts due to the relatively high weight of power generators.

When calculating specific impulse, only the propellant that is expended is counted. For a chemical rocket the propellant therefore would include both fuel and oxidizer; for air-breathing engines only the fuel is counted, not the 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
 29,420 3,000 433
Solid rocket
 2,452 250 3.005
Bipropellant liquid rocket
 4,413 450 9.737
Ion thruster 29,420 3,000 433
VASIMR 294,200 30,000 43,277

An example of specific impulse is 453 seconds, or, equivalently, 4442 N·s/kg or an effective exhaust velocity of 4442 m/s, for the Space Shuttle Main Engines when operating in vacuum.

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 jet engines, which get the oxidizer from the air always have greater range in the atmosphere than rockets.

The highest specific impulse for a chemical propellant ever test-fired in a rocket engine was lithium, fluorine, and hydrogen (a tripropellant): 542 seconds (5315 m/s). However, this combination is impractical, see rocket fuel.

Nuclear thermal rocket engines differ from conventional rocket engines in that the heat does not come from a chemical reaction. A nuclear rocket operates by passing pressurized hydrogen gas over a superheated nuclear core. Testing in the 1960s yielded a specific impulse of about 850 seconds (8336 m/s), about twice that of the Space Shuttle engines.

There are other non-rocket propulsion methods. The Hall effect thruster on the Smart 1 satellite has a specific impulse of 1640 s (16100 m/s) but a maximum thrust of only 68 millinewtons. The hypothetical Variable specific impulse magnetoplasma rocket (VASIMR) propulsion should yield 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] Calculations using MathCad

Wikipedia correctly explains lbf, lb, and even slug. These are commonly employed in engineering calculations that use the U.S. system of units. A worker must keep track of units to be sure of getting correct answers. MathCad knows the difference between lb and lbf and is unforgiving of their misuse. If MathCad is used, SI units, seconds for ISP, propellant rate in kg/s and include g, both magnitude and units in the calculated thrust (newton) come out right. With U.S. units, seconds for ISP, propellant rate in lb/s and include g (MathCad uses g for standard gravity and lb for pound mass), both magnitude and units are correct in the calculated thrust (lbf). If you delete g and have ISP in lbf·s/lb and propellant rate in lb/s using U.S. or N·s/kg and propellant rate in kg/s using SI, both magnitude and units are correct in the calculated thrust (lbf, newton).

[edit] Thrust calculations

For all vehicles thrust can be calculated using specific impulse and flow rate using the following equation[6]:

\mathrm{F_{\rm thrust}}=I_{\rm sp} \cdot \frac{\Delta m} {\Delta t} \cdot g_{\rm 0} \,

where:

Fthrust is the thrust obtained from the engine, in newtons (or poundals).
Isp is the specific impulse in seconds.
\frac {\Delta m} {\Delta t} is the mass flow rate in kg/s (or weight rate in lbf/s).
g0 is the standard acceleration of gravity: 9.80665 m/s² (or 32.174 ft/s²).

When working with U.S. units, divide both sides of the equation by g0 so that the left hand side of the equation becomes the thrust in lbf rather than poundals. Note that the thrust in lbf is also obtained by setting g0 to dimensionless 1. Note also that if the units of specific impulse are N·s/kg and the propellant rate is kg/s the calculated force is in newtons if g0 is set at dimensionless 1.

This formulation 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.

The specific impulse of various hydrocarbon fueled thrust engines
The specific impulse of various hydrocarbon fueled thrust engines

[edit] How specific impulse is determined

Specific impulse is determined by test. Specific impulse in seconds is the impulse in N·s (lbf·s) divided by the product of the mass of propellant consumed in kg (slug) and standard gravity:

I_{\rm sp}=\frac{\int \mathbf{F}\, dt }{m \cdot g_{\rm 0}}

Where:

Isp is the specific impulse in seconds
\int \mathbf{F}\, dt is the total impulse during the test, N·s (lbf·s)
m is the mass of the propellant consumed during the test, kg (slug)
g0 is the standard acceleration of gravity: 9.80665 m/s² (32.174 ft/s²)

[edit] Effect of ambient pressure on Specific Impulse

Rockets exhaust through a nozzle. Specific impulse is directly proportional to the thrust coefficient of the nozzle. Nozzle thrust coefficient is defined as thrust/throat area/chamber pressure. The nozzle thrust coefficient is primarily dependent on its expansion ratio which may or may not be fixed. Expansion ratio is the ratio of exit area to throat area. Maximum thrust (and Isp) is obtained when the nozzle expansion ratio is such that exit pressure matches the ambient pressure. Thus fixed expansion-ratio nozzles on rockets that substantially change altitude and thus ambient pressure during firing are usually over-expanded at low altitude resulting in lower Isp (and characteristic shock diamonds in the exhaust) than would occur if exit pressure matched ambient. They become under-expanded at high altitude (so the exhaust flares) which also results in lower Isp than would occur if the expansion ration were large enough for exit pressure to match ambient pressure. All nozzles are under-expanded in the vacuum of space but ambient vacuum gives the highest possible Isp for any nozzle. The best expansion ratio for nozzles in a vacuum is determined by a trade-off of specific impulse and nozzle weight.

[edit] References

  1. ^ Marks' Mechanical Engineers Handbook Sixth edition, p. 7-50
  2. ^ Fundamentals of rocket propulsion, p. 73, by Raymond E. Wiech, Jr. and Robert F. Strauss Imprint New York, Reinhold (1960)
  3. ^ CRC Handbook of tables for Applied Engineering Science ISBN 0-87819-252-2 p. 576
  4. ^ Rocket Propulsion Elements, 5th Edition, p. 22, George P. Sutton
  5. ^ Rocket Propulsion Elements, 5th Edition, p. 42, George P. Sutton
  6. ^ Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz

[edit] See also

fr:Impulsion spécifique ja:比推力 nl:Specifieke impuls pl:Impuls właściwy ru:Удельный импульс

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