Specific impulse

Specific impulse (usually abbreviated Isp) is a measure of how efficiently a <a href="/facts/Reaction_mass/xQ8dToB5">reaction mass</a> engine, such as a <a href="/facts/Rocket_engine/XT5gaFAb">rocket</a> using propellant or a <a href="/facts/Jet_engine/CJjFpeqt">jet engine</a> using fuel, generates <a href="/facts/Thrust/EM04CqV7">thrust</a>. In general, this is a ratio of the <a href="/facts/Impulse_(physics)/maePm9Ua">impulse</a>, i.e. change in momentum, per mass of propellant. This is equivalent to "thrust per massflow". The resulting unit is equivalent to velocity. If the engine expels mass at a constant exhaust velocity 
 
 
 
 
 v
 
 e
 
 
 
 
 {\displaystyle v_{e}}
 
 then the thrust will be 
 
 
 
 
 T
 
 =
 
 v
 
 e
 
 
 
 
 
 
 d
 
 m
 
 
 
 d
 
 t
 
 
 
 
 
 {\displaystyle \mathbf {T} =v_{e}{\frac {\mathrm {d} m}{\mathrm {d} t}}}
 
. If we integrate over time to get the total change in momentum, and then divide by the mass, we see that the specific impulse is equal to the exhaust velocity 
 
 
 
 
 v
 
 e
 
 
 
 
 {\displaystyle v_{e}}
 
. In practice, the specific impulse is usually lower than the actual physical exhaust velocity inefficiencies in the rocket, and thus corresponds to an "effective" exhaust velocity. 
That is, the specific impulse 
 
 
 
 
 I
 
 
 s
 p
 
 
 
 
 
 {\displaystyle I_{\mathrm {sp} }}
 
 in units of velocity *is defined by*

T
 
 
 a
 v
 g
 
 
 
 
 =
 
 I
 
 
 s
 p
 
 
 
 
 
 
 
 d
 
 m
 
 
 
 d
 
 t
 
 
 
 
 
 {\displaystyle \mathbf {T_{\mathrm {avg} }} =I_{\mathrm {sp} }{\frac {\mathrm {d} m}{\mathrm {d} t}}}
 
,
where 
 
 
 
 
 
 T
 
 
 a
 v
 g
 
 
 
 
 
 
 {\displaystyle \mathbf {T_{\mathrm {avg} }} }
 
 is the average thrust.
The practical meaning of the measurement varies with different types of engines. Car engines consume onboard fuel, breathe environmental air to burn the fuel, and react (through the tires) against the ground beneath them. In this case, the only sensible interpretation is momentum per fuel burned. Chemical rocket engines, by contrast, carry aboard all of their combustion ingredients and reaction mass, so the only practical measure is momentum per reaction mass. Airplane engines are in the middle, as they only react against airflow through the engine, but some of this reaction mass (and combustion ingredients) is breathed rather than carried on board. As such, "specific impulse" could be taken to mean either "per reaction mass", as with a rocket, or "per fuel burned" as with cars. The latter is the traditional and common choice. In sum, specific impulse is not practically comparable between different types of engines.
In any case, specific impulse can be taken as a measure of efficiency. In cars and planes, it typically corresponds with fuel mileage; in rocketry, it corresponds to the achievable <a href="/facts/Delta-v/eM4TaG9d">delta-v</a>, which is the typical way to measure changes between orbits, via the <a href="/facts/Tsiolkovsky_rocket_equation/S4HGsd56">Tsiolkovsky rocket equation</a>

Δ
        v
        =
        
          I
          
            
              s
              p
            
          
        
        ln
        ⁡
        
          (
          
            
              
                m
                
                  0
                
              
              
                m
                
                  f
                
              
            
          
          )
        
      
    
    {\displaystyle \Delta v=I_{\mathrm {sp} }\ln \left({\frac {m_{0}}{m_{f}}}\right)}

where 
 
 
 
 
 I
 
 
 s
 p
 
 
 
 
 
 {\displaystyle I_{\mathrm {sp} }}
 
 is the specific impulse measured in units of velocity and 
 
 
 
 
 m
 
 0
 
 
 ,
 
 m
 
 f
 
 
 
 
 {\displaystyle m_{0},m_{f}}
 
 are the initial and final masses of the rocket.

Specific impulse open-in-new

Specific impulse