Faster Times to Alpha Centauri – Part I

If fusion, assisted by magnetic sails, gets us to Alpha Centauri in ~50 years, then how do we get there faster? Absent annihilation drives, powered by gamma-ray lasing matter-antimatter reactions or Hawking decaying force-fed mini-black holes, then we need to get the power-supply off the space vehicle and send fuel, momentum and energy to the vehicle as it accelerates. “Centauri Dreams” has covered a number of notable options just recently – the laser-powered ramjet, the laser-powered rocket and, of course, the Bussard ramjet itself.

Then there’s the various light, laser, microwave and momentum sails that have been proposed over time. Jim Benford, twin brother of SF-writer Greg Benford, and high-power microwave expert, has studied in some detail the economics of microwave propelled interstellar sails. The costs are extra-ordinary for all but the most primitive interstellar probes, but such figures are somewhat misleading. A basic assumption is that the energy generating and emitting systems will be installed in much the same way we do things at present – Jim factors in economies of scale, but not revolutions in technique.

Let’s have a look at the raw requirements. We’ll assume a 1,000 tonne payload, 1,000 tonne mag-sail and 400 tonnes of laser-sail. A 5,000 terawatt laser accelerates the sail to 0.5c in about 0.8 years – a total energy expenditure of 1.26E+23 joules. How much power is 5,000 terawatts? Earth receives 174,400 terawatts from the Sun, absorbing 122,200 terawatts of that. Balancing out the heat-flows in Earth’s atmosphere and oceans, equator-wards of the Tropics is a region that gains energy, while pole-wards of the Tropics are regions which lose net energy back into space. Energy flows northwards and southwards via the winds and oceans – the winds carrying about 5,000 terawatts in both directions. Thus our laser-sail needs about 50% of the Earth’s wind-power available.

We can’t power a starship with Earth-based energies, unless we mine heroic amounts of deuterium or boron from the oceans and land. We must turn to what’s available in space – the most abundant source being the Sun. In radiant energy alone, the Sun puts out ~384.7 tera-terawatts (384.7 yottawatts), but also sends forth immense amounts of energy in the Solar Wind. Tapping either is a non-trivial task. In the late 1970s NASA and the US DoE studied Solar Power Satellites (SPS) – one estimate was that a 5 gigawatt SPS would mass ~50,000 tonnes. Thus 5,000 terawatts would require 1 million SPS with a total mass of ~50 billion tonnes. Of course techniques have improved considerably since the 1970s – some ultra-light SPS designs approach ~1,000 tonnes per gigawatt. To go much lighter we need to move them closer to the Sun – if we can operate them at 1,000 K then we can park them just 0.1 AU from the Sun. There our “1 gigawatt” SPS can generate 100 gigawatts. Thus ~5 million tonnes of near-Solar SPS will power the lasers for our starships.

How fast can we get there with 5,000 terawatts of laser-power pushing us? I’ll have some answers in Part II.

Fastest Time to Alpha Centauri – III

a repost from Facebook.

?”Daedalus” had a top speed of ~0.122c, though some variants could hit 0.138c for an extra 10,000 tonnes of fuel or so. This makes for a 36 year trip to Alpha Centauri – but no way of stopping. Equipping “Daedalus” with a magnetic sail and enough propellant to brake downwards from 1500 km/s, when the mag-sail performance drops significantly, lets us contemplate braking to a halt. But, as always for realistic rockets, there’s a trade off between how fast the fuel can be expelled – the mass-flow rate – and the cruise speed. Too high a cruise speed means the time spent accelerating drags out and actually reduces the average speed.

Throwing in the relevant characteristics and model parameters means that I can compute the total flight time for a range of speeds, and then search for the minimum time. I’ve assumed a 1,000 tonne mag-sail which is about equal in mass to the “Daedalus” 2nd Stage with enough propellant for the final brake phase, 1100 tonnes. The mag-sail is 800 km in radius and carries a super-current of several hundred kiloamps. The maximum magnetic field in the wire is about 16 tesla, which is high, but not as high as the critical field of some present day SCs.

What results is a minimum flight time of 45 years – not much more than the bare minimum. The cruise speed is a higher 0.1388c, while the initial mass is 181,480 tonnes. In the original “Daedalus” plan mining 50,000 tonnes of propellant from Jupiter would take 20 years. To mine the extra 130,000 tonnes needed for a faster probe could require ~60 years. However going a bit slower means a 50 year flight needing only 66,040 tonnes initial mass.

Fastest Time to Alpha Centauri – Two-Stage Mag-Sail Scenario

After rearranging the mass-models, just for the sake of the exercise (Eric Storm’s suggestion), I’ve computed the fastest time to Alpha Centauri via a Mag-Sail equipped Two-Stage “Daedalus”. In this case both stages will be use to reach the cruise speed, then the mag-sail will be deployed at the appropriate point in the voyage. The minimum trip-time is when the cruise-speed is 0.13488c, the mission time 45.82 years and an initial mass of 181,480 tonnes. So, yes, Alpha Centauri can be reached in under 50 years by “Daedalus”. Interestingly exactly 50 years needs a mass of 66,040 tonnes (this includes the 1,000 tonne mag-sail.)

How far can it reach in under 100 years? About Tau Ceti’s distance – 11.9 ly. To reach GJ 581c requires ~152 years and about 540,000 tonnes initial mass, minimum. For the same mass as the minimum time to Alpha Centauri, the trip to GJ 581c takes 164 years. Patience is required, it seems.

Fastest Time to Alpha Centauri – Errata Nipped in the Bud

Blogging helps collect one’s thoughts. After the previous post I revisited my presentation and mass-models, only to discover a significant mistake in a key cell reference in Excel. Yikes! Re-writing my equations’s references I managed to shave a significant number of years off the minimum voyage time to Alpha Centauri via a mag-sail equipped “Daedalus” 2nd Stage. And update the affected slide being presented by my friend Pat Galea (thanks again, Pat!)

Now I am really interested in what a two-stage “Daedalus”+Mag-Sail can do. More importantly, how far can we send it in 100 years? As fascinating as Alpha Centauri A & B (and Proxima) might be, the known exoplanets are all much further away. The nearest (arguably) habitable exoplanet is Gliese 581g at a distance of 20.3 light-years. Can we get there in under 100 years using fusion and mag-sails? Or do we need something different?

Fastest Time to Alpha Centauri – Errata

Something about my mass model of “Daedalus” didn’t sit right with me, so I recomputed the tankage from first principles. The percentages were more like 5%, thus meaning a slightly slower fastest time – 71.58 years with an initial mass of 281,181 tonnes.

While “Daedalus” can cruise at 0.12-0.14c, meaning speedy trips to Alpha Centauri, compared to the above, the problem is that there’s no way of stopping at such speeds – finite tank mass means an infinite mass of propellant would be required.

I went on to compute the performance of a magnetic sail equipped vehicle and got quite an encouraging result – which I’ll post here after the Symposium presentation itself, which is in a matter of days. Traveling to Alpha Centauri via fusion rocket in sub-50 years will be an immense engineering challenge, so one hopes better options will arise. Jonathan Vos Post has a paper online which is a good example of the extreme performance required for very rapid flybys – a perfectly efficient fusion motor, a five stage vehicle, and a mass-ratio of ~100,000 means a flight in ~9 years or so. Wildly unrealistic, but illustrative of the effort needed.

To do better will need something better than rockets, but not necessarily more powerful than fusion energy.