Since I had a hard time finding the formulas for determining the efficiency Ram-Augmented Interstellar Rocket propulsion, I thought I'd derive it's performance on a theoretical basis.

For those of you who aren't familiar, a Ram-Augmented Interstellar Rocket (or RAIR) is kind-of like a Bussard interstellar ramscoop, except instead of using the scooped-up interstellar medium for fuel it uses itonlyfor reaction mass. This gets around the Bussard fusion-fuel ramscoop's main problem: if you want to inject the incoming interstellar hydrogen into your fusion reactor, you have toslow it down(relative to your spacecraft). You can't expect to shoot it into your fusion chamber at 1/10 of the speed of light and not run into insurmountable problems. By slowing the incoming material down, though, you're causingdrag. Your spacecraft's top speed could never exceed its own exhaust velocity! So, by using the scooped-up matter ONLY as reaction mass to push against, you no longer need to slow it down, and you could hypothetically use it as extra reaction mass to make your engines more efficient.

Or ...could you?Would it actually help?

My main (optimistic) assumption was that you had a perfectly efficient nuclear fusion engine, which could fuseallof your onboard hydrogen fuel into helium, and allocateallthe energy from this burning process in any ratio you desire between your helium fusion products and the incoming ram-scooped reaction mass.

You immediately run into two big problems:

1. The interstellar medium isextremely thin. In the "local fluff" in which the sun and a few neighboring stars are embedded, the density of the interstellar medium is only about 1 atom of hydrogen for every 10 cubic centimeters. (Outside the local fluff it's even worse.) This means that if your starship had aridiculouslyhuge 1000 km radius scooping field, at 10% of the speed of light you'd only be scooping up15 gramsof hydrogen per second. Even a modest spacecraft would have to weigh in at at least 100 tonnes empty to carry anything even remotely interesting, and that's theemptymass, before the mass of your unexpended fuel is added in. Even with perfect hydrogen-to-helium nuclear fusion (assumingnoram-assist), you'd be burning about an ounce of fuel (28 grams) every second to accelerate that 100 tonne spacecraft at 1g. That's nearly twice the mass of material you're scooping in for "reaction mass". And realistically, if your mission calls for you to go significantly faster than 10% of light speed, your fuel load at 10% of light speed is going to atleastdouble your spacecraft's mass, so you'd actually have to burn at least twice this much fuel.

2. The reaction mass isn't standing still when you scoop it in. It's zipping down your gullet at 30,000 kilometers per second. What does this mean from the standpoint of the Conservation of Energy, and the Conservation of Momentum? It means it's going to take ahellof a lot more energy to impart a given amount of momentum to 15 grams ofthismatter, than it will to impart the same amount of momentum to the spent fuel products (which at the moment of burning are travelling along with you at the same speed as your spacecraft).

This second one is the big killer. How much more energy does it take? Well, for your normal exhaust, the kinetic energy you'll have to add to get a mass m up to a speed v is:

E = 0.5 m v^{2}

...becauseit starts out with a velocity of 0.But, the ram-scooped material starts out with a velocity of 30,000,000 meters per second. So if the same energy E were applied toit, the formula to determinehow much fasterit's going afterward (dv) becomes:

E = 0.5 m (30,000,000 m/s + dv)^{2}- 0.5 m (30,000,000 m/s)^{2}

Note that the magnitide difference between v and dv is independent of the size of m.It would not matter even if interstellar space were filled with bowling balls.That second equation will always be less efficient than the first. Convert it to momentum in a variety of cases, and see for yourself!

And this is even assuming that you've completely overcome the drag problem and that the incoming material can be scooped up withnodrag at all.

Bottom line: With perfect nuclear fusion, where the energy released can be routed entirely into kinetic energy of your fusion products or the ram-scooped mass or both, RAIR buys younothing.

It might be useful for braking and refuelling near the end of the voyage, but as an acceleration trick it's worthless.