Thermodynamics and Propulsion

11.4 Other expressions for efficiency - $I_{sp}$ and SFC

Sometimes the overall efficiency of aircraft engines is expressed in alternative parameters: specific impulse, $I$ , and thrust specific fuel consumption, TSFC or just SFC. Both of these parameters measure how effectively fuel is used, and have dimensions.

Specific Impulse ($I$ or $I_{sp}$ ):

$$I_{sp} = \frac{\textrm{thrust}}{\textrm{fuel weight flow rate}} \qquad \textrm{(units of seconds)}$$

$$= \frac{F}{\dot{m}_f g} =\frac{F}{f \dot{m}g},$$

where $\dot{m}_f =f\dot{m}$ is the fuel mass flow rate. To find the fuel-air ratio, $f$ , we employ a control volume around the combustor and carry out an energy balance.

Specific Fuel Consumption (SFC or TSFC):

$$SFC = \frac{\textrm{mass flow rate of fuel}}{\textrm{thrust}} \qquad \textrm{(units of lbm/hr/lbf or kg/s/N)}$$