= Specific impulse
{title2=$I_{\rm sp}$}
<Specific impulse> measures the <impulse> delivered by a rocket per unit propellant consumed. In its conventional seconds form, divide total axial <thrust> impulse by propellant mass $m_p$ and <standard gravity> $g_0$:
$$
I_{\rm sp}=\frac{\int_0^T F(t)\,dt}{m_p g_0},\qquad m_p=\int_0^T\dot m(t)\,dt.
$$
For constant conditions this becomes $I_{\rm sp}=F/(\dot m g_0)$, where $\dot m$ is the positive expelled <mass flow rate>. Multiplying by $g_0$ gives the effective <exhaust velocity>. The conventional value $g_0=9.80665\,\mathrm{m\,s^{-2}}$ is a unit convention, not a requirement that the engine operate near Earth.<Specific Impulse by NASA Glenn Research Center>[Total Impulse and displayed specific-impulse definitions]{ref} https://www.nist.gov/system/files/documents/srd/jpcrd574.pdf[Section2.6, equation30, conventional standard acceleration of gravity]{ref}
For a worked example, a steady $6000\,\mathrm N$ engine consuming $2\,\mathrm{kg\,s^{-1}}$ has $I_{\rm sp}\approx305.9\,\mathrm s$ and effective <exhaust velocity> $3000\,\mathrm{m\,s^{-1}}$. A ten-second firing supplies $60000\,\mathrm{N\,s}$ using $20\,\mathrm{kg}$ of propellant. The unit of seconds does not mean that this engine can burn for 305.9 seconds: duration also depends on the available propellant and its flow rate.
In a laboratory illustration, integrate the force recorded on a calibrated engine stand and measure the mass consumed during the same firing. Report the ambient <pressure>, since nozzle pressure forces contribute to <thrust>. At fixed <specific impulse>, doubling the <mass flow rate> doubles <thrust>; a large <specific impulse> alone does not specify a large force. For varying performance, the burn-integrated value is weighted by propellant flow, rather than generally equaling a simple time average.
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