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Exhaust velocity is the velocity of expelled propellant measured relative to the engine. In a simple straight jet it points backward, while the engine's thrust points forward. Rocket calculations often use its positive magnitude, as in rocket exhaust speed. The relative frame matters: the propellant can be moving forward relative to a distant observer while still leaving the engine backward.

For a steady rocket nozzle with outward mass flow rate $\dot{m}>0$, exit speed $u_e$, exit pressure $p_e$, ambient pressure $p_a$ and exit area $A_e$, the axial thrust isThe pressure term motivates an effective exhaust velocity $v_e=F/\dot{m}$, which includes both momentum flux and nozzle pressure effects. When exit and ambient pressures match, $v_e=u_e$. Specific impulse in seconds is $I_{\mathrm{sp}}=v_e/g_0$, where $g_0=9.80665\mathrm{m}{\mathrm{s}}^{-2}$ is conventional standard gravity; using this unit does not imply that the engine must operate near Earth.^[ref]

For an illustrative pressure-matched engine, $\dot{m}=2\mathrm{kg}{\mathrm{s}}^{-1}$ and $u_e=3000\mathrm{m}{\mathrm{s}}^{-1}$ give $F=6000\mathrm{N}$. At the same effective exhaust velocity, halving the mass flow rate halves thrust. For an ideal burn without external forces and with constant $v_e$, the rocket equation gives $\Delta v=v_e\ln (m_0/m_f)$: a mass ratio of $2$ yields approximately $2079\mathrm{m}{\mathrm{s}}^{-1}$. Thus higher effective exhaust velocity increases the velocity change available from a specified propellant fraction; it does not by itself specify a large thrust.

Ion propulsion produces thrust by using electrical energy to accelerate ions out of a spacecraft. In a gridded ion engine, a discharge creates ions from propellant such as xenon, electric fields accelerate them through grids, and a neutralizer supplies electrons so the departing beam does not leave the spacecraft progressively charged. The exhaust carries momentum; no surrounding air is required.^[ref]

For an ideal directed exhaust with mass flow rate $\dot{m}$ and exhaust velocity $v_e$, neglecting the pressure term,Here $P$ is electrical input power and $\eta$ the fraction converted into directed exhaust kinetic energy. Thus high exhaust speed saves propellant for a given momentum change but reduces thrust at fixed power. At $P=1\mathrm{kW}$, $\eta =0.6$ and $v_e=30\mathrm{km}{\mathrm{s}}^{-1}$, the ideal thrust is $0.04\mathrm{N}$.

Ground tests operate the engine in a pumped vacuum chamber, measuring beam current, power, propellant flow and thrust. A bright plume alone cannot establish efficiency or delivered impulse. NASA's Deep Space 1 and Dawn missions demonstrated sustained ion propulsion in flight, where small thrust accumulated over long operating times.^[ref]

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 $g_0$:For constant conditions this becomes $I_{\mathrm{sp}}=F/(\dot{m}{g}_0)$, where $\dot{m}$ is the positive expelled mass flow rate. Multiplying by $g_0$ gives the effective exhaust velocity. The conventional value $g_0=9.80665\mathrm{m}{\mathrm{s}}^{-2}$ is a unit convention, not a requirement that the engine operate near Earth.^{[ref] [ref]}

For a worked example, a steady $6000\mathrm{N}$ engine consuming $2\mathrm{kg}{\mathrm{s}}^{-1}$ has $I_{\mathrm{sp}}\approx 305.9\mathrm{s}$ and effective exhaust velocity $3000\mathrm{m}{\mathrm{s}}^{-1}$. A ten-second firing supplies $60000\mathrm{N}\mathrm{s}$ 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.