Editing Specific impulse (section)

===Specific impulse in seconds===
{{Refimprove section|date=August 2019}}
Specific impulse, measured in seconds, can be thought of as how many seconds one kilogram of fuel can produce one kilogram of thrust. Or, more precisely, how many seconds a given propellant, when paired with a given engine, can accelerate its own initial mass at 1&nbsp;g. The longer it can accelerate its own mass, the more delta-V it delivers to the whole system.

In other words, given a particular engine and a mass of a particular propellant, specific impulse measures for how long a time that engine can exert a continuous force (thrust) until fully burning that mass of propellant. A given mass of a more energy-dense propellant can burn for a longer duration than some less energy-dense propellant made to exert the same force while burning in an engine. Different engine designs burning the same propellant may not be equally efficient at directing their propellant's energy into effective thrust. 

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

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<math display="block">I_{sp} = \frac{F_{avg}}{\dot{m} \cdot g_{0}}</math>
Where:
*<math>I_\text{sp}</math> is the specific impulse (seconds),
*<math>F_{avg}</math> is the ''average'' thrust ([[newton (unit)|newton]]s, [[Kilogram-force|kilograms-force]] or [[pound (force)|pounds-force]]),
*<math>\dot m</math> is the [[mass flow rate]] of the propellant (kg/s or [[slug (unit)|slug]]s/s),
*<math>g_0</math> is the [[standard gravity]] (defined as {{cvt|9.80665|m/s2||sigfig=7|disp=x|, which is about }}).
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<math display="block">I_{sp} = \frac{I_{total}}{m \cdot g_{0}}</math>
Where:
*<math>I_\text{sp}</math> is the specific impulse (seconds),
*<math>I_{total}</math> is the [[Impulse (physics)|total impulse]] ([[Newton-second|newton-seconds]], kg⋅m/s or lbf⋅s),
*<math>m</math> is the mass of the used propellant (kilograms or pounds),
*<math>g_0</math> is the [[standard gravity]] (defined as {{cvt|9.80665|m/s2||sigfig=7|disp=x|, which is about }}).
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''I''<sub>sp</sub> in seconds is the amount of time a rocket engine can generate thrust, given a quantity of propellant the weight of which is equal to the engine's thrust.

The advantage of this formulation is that it may be used for rockets, where all the reaction mass is carried on board, as well as airplanes, where most of the reaction mass is taken from the atmosphere. In addition, giving the result as a unit of time makes the result easily comparable between calculations in SI units, imperial units, US customary units or other unit framework.

[[File:Specific-impulse-kk-20090105.png|thumb|center|upright=3.2|The specific impulse of various jet engines (SSME is the [[Space Shuttle Main Engine]])]]

====Imperial units conversion====
The [[English unit]] [[Pound (mass)|pound mass]] is more commonly used than the slug, and when using pounds per second for mass flow rate, it is more convenient to express standard gravity as 1 pound-force per pound-mass. Note that this is equivalent to 32.17405 ft/s2, but expressed in more convenient units. This gives:

<math display="block">F_\text{thrust} = I_\text{sp} \cdot \dot m \cdot \left(1 \mathrm{\frac{lbf}{lbm}} \right).</math>

====Rocketry====
In rocketry, the only reaction mass is the propellant, so the specific impulse is calculated using an alternative method, giving results with units of seconds. Specific impulse is defined as the thrust integrated over time per unit [[weight]]-on-Earth of the propellant:<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]]|access-date=22 December 2009}}</ref>

<math display="block">I_\text{sp} = \frac{v_\text{e}}{g_0},</math>

where

*<math>I_\text{sp}</math> is the specific impulse measured in seconds,
*<math>v_\text{e}</math> is the average exhaust speed along the axis of the engine (in m/s or ft/s),
*<math>g_0</math> is the [[standard gravity]] (in m/s<sup>2</sup> or ft/s<sup>2</sup>).

In rockets, due to atmospheric effects, the specific impulse varies with altitude, reaching a maximum in a vacuum. This is because the exhaust velocity is not simply a function of the chamber pressure, but is [[de Laval nozzle|a function of the difference between the interior and exterior of the combustion chamber]]. Values are usually given for operation at sea level ("sl") or in a vacuum ("vac").