Specific Impulse and Exhaust Velocity

Specific Impulse I_s is defined as exhaust velocity V_e divided by gravitational acceleration at Earth's surface, g (which is 9.81 m/s^2): $$ I_s = \frac{V_e}{g} $$

To use specific impulse in Tsiolkovsky's Rocket Equation, we need to multiply it with g. $$ \Delta V = I_s g \times ln\left(\frac{m_1}{m_2}\right) $$

But why do this? Why not just use the exhaust velocity? We already know higher exhaust velocities are more efficient and produce higher delta V for given amount of fuel.

Well, partly because it's a way to compare different propulsion technologies. For example solar sails aren't rockets, so we can't really talk about exhaust velocities. But we can talk about its specific impulse, which is analogous to efficiency of propulsion.

We can compare different rocket engines that have different fuel/oxidizer pumping technologies.

Specific impulse indicates how much delta v is produced for a given amount of fuel, if we're talking about rockets.

Liquid fuel engines are broadly categorised into "open cycle" and "closed cycle".

Open and Closed Cycle Liquid Fuel Rocket

In "open cycle", some fuel and oxygen are burned in a little turbine that drives the main pump. The main pump pushes fuel and oxygen into the main combustion chamber to be burned and produce thrust. But the fuel and oxygen that powered the pump are just disposed of and does not contribute to the thrust.

In "closed cycle", it is as before, but the burned fuel/oxygen used to drive the pump is fed into the main combustion chamber and contributes to the thrust.

Now, in both cases, the fuel used is the same, the combustion temperature is the same, the nozzle shape is the same. Thus strictly speaking, they both have the same exhaust velocity. But the closed cycle has a higher specific impulse than the open cycle, because all the fuel contributes to thrust.

Open cycle engines use more fuel to attain the same delta v because some of it is dumped after using it to power the pump. It has lower specific impulse, which has the effect analogous to having lower exhaust velocity, even though it actually has the same exhaust velocity, if using the same fuel and nozzle.

On the other hand, closed cycle engines are harder to build. You're trying to feed burned fuel into a high pressure combustion chamber. You could get backwash if you're not careful. High pressure gas from the combustion chamber forcing back into the turbine.

Nuclear Thermal Rocket

Nuclear thermal rockets are interesting. Instead of heating the gas by burning fuel and oxygen, they use a nuclear reactor to heat up the gas. You could get higher gas temperatures than by burning, and thus higher exhaust velocity, and thus higher specific impulse. It's featured in science fiction books such as 2001: A Space Odyssey and 2010: Odyssey Two.

Specific impulse indicates how much delta v is produced for a given amount of fuel, if we're talking about rockets.

Solar Sail

For things like solar sails... It doesn't carry fuel. It's a big reflective foil pushed by light from the sun! Its specific impulse is *infinite*. On the other hand, the push is very weak. It takes a very long time to get to the velocity you want, and you can't fight gravity.


Artist drawing of Cosmos 1 Solar Sail

Anyway here's a little table with an open loop, closed loop, ion engine, solar sail, nuclear-thermal. Source from Wikipidea and Encyclopedia Astronautica.

Engine/Propulsion Specific Impulse Exhaust Velocity Thrust
Liquid fueled
(Open cycle)
Liquid fueled
(Closed cycle)
Nuclear Thermal
Ionic Propulsion
Solar Sail

Index