Looking for figures for contemporary interstellar engine options

Question

So I have already done... a lot of reading on this subject lately. A lot. You wouldn't believe. My maths is... functional, probably far above 'average', but when it gets into the realms of the 'rocket equation' and relativistic effects I pretty much have to take what I'm reading for granted. Problems arise when I read two different essays that each end up contradicting each other.

For example, I read in one place that the maximum possible velocity for a chemical rocket is 5km/s. But I'm fairly sure that's not the case, except perhaps that's the maximum velocity of rockets currently in production, due to fuel-tank sizes?

But anyway, to cut things a little short (too late I know) - I have found and read the 'relativistic rocket' text, which seems to be sent around a fair bit on here as a good source of information, as well as a couple other similar pages and essays. However these all only give data for either hypthetical "100% efficient engines", or for antimatter engines, or in some cases a 100% efficient antimatter engines. None of which is helpful, as they don't actually exist.

What I am looking for is essentially the same information, but for either the best Ion drive engine we currently have (known prototypes are allowed), and/or the best chemical or more traditional 'rocket' type engines we have.

What I am looking for is - (for both the ion and rocket)

• Amount of fuel/propellant needed to get the ship up to 0.05C (and then back down to stationary) for a 4.7ly trip.
• Same question, but for 0.2C.
• What the maximum acceleration would be (mostly for ion)
• With a maximum acceleration of 9.8m/s, how long would the ship need to be accelerating for.

I know the relativistic rocket page has this information, but only for 'fake' engines. 10kg per 1kg of payload was a major answer I was looking for... but I need it for non-100% efficient engines. And I can't seem to convert it myself, as nowhere actually seems to list the efficiency of our current generation of engines! (They often list it as 100% efficient at certain points, but I assume thats relative to its own profile).

Hopefully this made vague sense... Pointing me in the direction of figuring out the answers would be great too!

Edit: Realised I didn't specify a vehicle mass. Reasoning for this is that I wanted a similar result as the Relativistic Rocket page, that gives it in KG of fuel per 1kg of payload. I assume in their calculations they take into account the fuel's own mass needing to be accelerated on top of the payload.

Answer 1

It’s completely impractical to get to even .05c with either chemical or ion rockets.

Here’s the rocket equation, rearranged to “mass fraction form”:

$$M_f = 1 - \frac{m_1}{m_0} = 1-e^{-\Delta V / v_\text{e}}$$

where $M_f$ is the propellant mass fraction (the part of the initial total mass that is turned into rocket exhaust).

The delta-v term is 15,000,000 m/s, and $v_e$ Is about 30,000 m/s for ion engines. The ratio there is 500, so you’re taking $e$ to the -500 power to get the payload fraction. That is, for every ton of fueled spaceship you launch, you’re getting something like 0.000 000 000 000 000 000 4 tons of payload up to top speed. (I think. My calculator doesn’t want to deal with that many zeros.)

It’s quite a bit worse for chemical rockets.

Fusion rockets theoretically can achieve substantially higher exhaust velocity, but the mass ratios are still pretty ridiculous.

Answer 2

Amount of fuel/propellant needed to get the ship up to 0.05C (and then back down to stationary) for a 4.7ly trip.

Russell Borogove covered this nicely above. The answer is unambiguously "too much". When your required delta-V exceeds your exhaust velocity, your mass ratio shoots up exponentially. 0.05c is pretty gosh-darn fast... about the speed that fusion reaction byproducts might be expected to travel. If you could manage to make a fusion rocket where most of the stuff you chucked into the reaction chamber could be persuaded to fuse, then you could reach this sort of velocity.

In practise, we a) can't actually do anything useful with fusion beyond making bombs and b) the various theoretical designs for fusion rockets have much, much lower exhaust velocities because the burnup fraction is low and the reaction products use up a big chunk of their energy heating up the unburnt fuel and other things like the mass of the liner or hohlraum. The HOPE MTF design, quite an optimistic one, only has an exhaust velocity of about 700km/s... still too slow by a factor of 20. The Icarus Interstellar Firefly design, even more wildly optimistic, would fit your mission profile very neatly. The original paper is paywalled, but Project Rho has a summary.

Same question, but for 0.2C.

If you want to do this with rockets, you'll need some antimatter. Lots of antimatter.

According to Frisbee, delta-V of an antimatter rocket (even assuming you can make and run such a thing) is difficult to raise above .25c, and you want a delta-V of .4c.

Basically the take-home message is that lightsails might seem bad, but the alternatives are all vastly more complex and will probably blow up and kill you.

What the maximum acceleration would be (mostly for ion)

I think Dawn managed about 6-7 microgees, but I think that 10-100x that should be achievable with fancier engine designs, assuming you can combine them with a suitable power supply (easier said than done, as you've observed in another recent question).

With a maximum acceleration of 9.8m/s, how long would the ship need to be accelerating for.

Slow enough to handwave away the inconvenient relativistic corrections, so a little under 18 days to get to .05c, and a little under 71 days to get to .2c. All you need is a magical rocket to provide all that power.

The more realistic "tenth of a milligee" option takes more like 480 years.