Specific Impulse and Exhaust Velocity

Specific impulse is the standard figure of merit for a rocket engine, and it is quoted in seconds, which is the single most confusing convention in the whole subject. It is not a burn time. It is not a duration of anything. It is impulse delivered per unit weight of propellant consumed, and once you divide newton-seconds by newtons the units reduce to seconds and the name sticks. An engine of 300 s specific impulse produces one newton of thrust for 300 seconds from one newton's worth of propellant weight.

The conversion to the velocity the rocket equation actually wants is one multiplication: $v_e = I_{sp} \, g_0$, where $g_0$ is standard gravity, exactly 9.80665 m/s² by definition. That number was fixed by the General Conference on Weights and Measures and it does not vary. It is not the local gravitational field. An engine does not gain specific impulse by being flown to the Moon, and computing Isp with the Moon's 1.62 m/s² produces a figure six times too large that cannot be compared with any published number for any engine ever built. This is the classic error in rocketry, and it is worth being blunt about: $g_0$ in this equation is a unit-conversion constant and nothing else.

Why keep such a strange unit at all? Because it survives the metric-imperial divide. Exhaust velocity is 4400 m/s or 14,435 ft/s depending on where you work; specific impulse is 448.7 seconds in both. That single fact kept the convention alive through the entire twentieth century, and it is why engines are still catalogued in seconds. Working values to keep in your head: solid motors 250–280 s, kerosene-oxygen 300–350 s, hydrogen-oxygen 380–460 s, ion thrusters 3000 s and beyond — though an ion engine's thrust is measured in millinewtons, which is the other half of that story.

Always ask which Isp you have been handed. Every engine has a SEA-LEVEL figure and a VACUUM figure, and the vacuum number is larger by 10 to 30% because ambient pressure has stopped pushing back on the nozzle exit. The gap widens with the nozzle's expansion ratio, so an upper-stage engine with a large bell shows the biggest difference of all. Quoting a vacuum Isp for a first-stage lift-off overstates both the thrust and the delta-v, and it is the second most common mistake in this subject after confusing $g_0$ with local gravity.