Specific Impulse

Welcome to rocket science! Specific impulse is a key performance metric for spacecraft propulsion systems. It is the rough equivalent of the more familiar 'miles per gallon' or 'kilometers per liter' measurements used on terrestrial vehicles. It is commonly written as I_sp.

So what is it?

In space, of course, there's no point in describing how far you can get on a certain amount of propellant, because there's no resistance to overcome. You can get as far as you want on whatever amount you'd care to use - if you have enough time to wait. The better measurement is that of what ability a spacecraft's engines have to change its velocity for a given amount of propellant, and (surprise) this is exactly what I_sp is.

It is expressed in seconds, and refers to the exhaust velocity of the spacecraft divided by g, or approximately 9.8 meters per second per second. The math, AFAIK, looks like this:

If:
• T = thrust
• V_e = exhaust gas velocity
• dm = delta-m, or change in mass
• dt = delta-t, or change in time
• dW = delta-W, or change in weight
• g = Earth's gravity, or 9.8 m/s²

then

T = V_e(dm/dt)

and, since

W = mg

then

(dW/dt) = g (dm/dt)

And, finally:

I_sp = T / (dW/dt) = V_e (dm/dt) / ( g (dm/dt)) = V_e / g

(whew.)

I_sp also is a direct representation of the tradeoff between power (represented in the rocket science area as thrust) and efficiency(I_sp) . For example, large powerful engines such as those required to boost vehicles out of the atmosphere have appallingly low I_sp ratings, but that does not matter because their design criteria is driven much more highly by power than efficiency. They typically have a burn time measured in minutes. On the other hand, if you are designing an engine to take a spacecraft to the outer solar system, or to another star system, you'd need an extremely high I_sp!

As an example, the Space Shuttle's Main Engines (SSME), which are some of the best-performing large chemical rockets that we can build today, have a specific impulse of around 500. To illustrate this, let's use some figures generated by NASA's Breakthrough Propulsion Physics group. Yep, you guessed it - some of your tax dollars (if you're American) go directly to a small group of folks trying to build a warp drive! (And a better use I can't imagine). Anyhow.

Take, as our desired flight plan, the ability to reach the nearest exsolar star (Proxima Centauri) in nine centuries. Note carefully that this assumes no mass for stopping once you get there, just that in nine centuries your vehicle would zip past Proxima at whatever velocity you'd achieved. Well, to do this on an I_sp of 500 (using the SSMEs) would take 10¹³⁷ kg of propellant (Hydrogen and Oxygen)! Unfortunately, there isn't enough mass in the universe to supply those engines. We'd need to do better.

A notional nuclear fission rocket, which heated propellant via nuclear reactions and threw it out the back a là TIMBERWIND, would have (according to NASA) an I_sp of around 5,000 seconds, or ten times that of the SSMEs. Well, that drops the requirements pretty far - down to 10¹⁷ kg of propellant. However, that volume would still fill around (Carl Sagan be with me) a billion conventional petroleum supertanker ships. Not too promising.

Well, how about fusion? That's another jump in efficiency! Doubling the specific impulse of the fission rocket to 10,000 sec, the fuel requirements drop to a paltry 10¹¹ kg. or a mere thousand supertankers. This is starting to get better, never mind that we can't build those yet. Finally, we could make the ultimate mass-to-energy jump and take a page from Star Trek to build a matter/antimatter rocket, or perhaps an ultra-efficient ion engine. These technologies are estimated (and in the case of the ion drive, measured) to have an I_sp of around 50,000 seconds, making our propellant demand around 10⁵ kg, or ten railway tanker cars full. That's not too bad.

Of course, now we're still taking 900 years to get there.

So this is what specific impulse is, and this is why it matters.