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.

Fastest Time to Alpha Centauri

Currently I am working on a paper & presentation for the 100 YSS Symposium in Houston, to be presented by an Icarus colleague. I am examining the effectiveness of using a magnetic-sail to brake to low-speeds in the target system, but part of that is a comparison with a pure fusion rocket. As it is still the most detailed design for an interstellar fusion rocket I am using the performance characteristics of the “Project Daedalus” star-probe. The most economical use of propellant for pure-fusion is to boost up to cruise speed using the 1st Stage, drop the spent stage, then brake using the 2nd Stage after a period of cruising. “Daedalus”, due to its ignition system and the tricky physics of implosion ignited fusion, had two different exhaust velocities for the stages – 1st Stage was 10,600 km/s and 2nd Stage was 9,210 km/s.

A limiting variable on the possible mass-ratio was the mass of the cryogenic tankage required to keep helium-3/deuterium fuel at a chilly 3 K storage temperature. For the 1st Stage the tankage was 2.85% of the fuel mass stored and 4% for the 2nd Stage. As a critical mass-ratio is approached the required mass of propellant goes asymptotic – runs off to infinity. Thus there’s a maximum cruise speed for a single stage using “Daedalus” style storage systems. It works out as 0.1c for the 2nd Stage engine. To achieve that speed requires infinite propellant mass, so it’s not really practical.

A more practical question is the fastest trip to a given destination. Rockets are limited in how quickly they can burn their fuel – Stage 1 burns it at 0.72 kg/s and Stage 2 burns it at 0.0711 kg/s. To achieve higher speeds requires burn-times that are asymptotically rising, when the critical mass-ratio is factored in.

Alpha Centauri is 4.36 light-years away. A two-stage “Daedalus” vehicle can travel there in 68 years at a maximum speed of 0.075c and then brake to a halt at the destination. However the amount of fuel required is about 300,000 tonnes. Going a bit slower – arriving in 71 years – can reduce the fuel required to just 140,000 tonnes. “Daedalus” carried an immense payload by modern standards – 450 tonnes, the equivalent of the International Space Station. The recent paper on boot-strapping a robotic economy on the Moon only required delivery of 41 tonnes to kick-start things. A large exo-solar industrial base could be sent to other star systems in a decent time frame to build, in advance of human arrival, large laser or mass-beam facilities to decelerate a human-carrying star-ship. Such would allow much faster trip-times.

The Way to K-II …Update

The preprint I mentioned is available online (thanks to Brian Wang’s “Next Big Future” post) and it’s here:
Affordable, rapid bootstrapping of space industry and solar system civilization

More discussion is coming. One preliminary idea is that 100,000 teleoperated robots on the Moon could have a volunteer Army controlling them to help build the Solar System economy. The pay-off for all involved would be long-term energy/resource security – and potential wealth.

ISV Venturestar

The only realistic Interstellar Starship from Hollywood so far

The ISV “Venturestar” is an example of “poly-propulsion”, using a Forward laser-sail to boost to 0.7c, and brake to a halt, in Sol-space, then using matter-antimatter, Powell/Pellegrino “Valkyrie” style, to brake at Alpha Centauri, then boost for the trip home.

The Way to K-II

No. Not the mountain in the Himalayas. Kardashev II Civilization status – a civilization using the energy output of its star. Earth intercepts just 2.2 billionths of the Sun’s energy and presently we use ~1/10,000th of what Earth receives. Thus the plateau of K-II seems a long way off. However we could boot-strap our way there by developing an automated space economy. And the first step isn’t huge.

Philip Metzger and Robert Mueller have both been busy developing a Map of the way to K-II via quasi-self-replicating robotics on the Moon.

Here’s Phil’s 2011 100 YSS Presentation: Nature’s Way of Making Audacious Space Projects Viable
Abstract

Building a starship within the next 100 years is an audacious goal. To be successful, we need sustained funding that may be difficult to maintain in the face of economic challenges that are poised to arise during these next 100 years. Our species’ civilization has only recently reached the classification as (approximately) Type-I on the Kardashev scale; that is, we have spread out from one small locality to become a global species mastering the energy and resources of an entire planet. In the process we discovered the profound truth that the two-dimensional surface of our world is not flat, but has positive curvature and is closed so that its area and resources are finite. It should come as no surprise to a Type I civilization when its planet’s resources dwindle; how could they not? Yet we have gone year by year, government by government, making little investment for the time when civilization becomes violent in the unwelcome contractions that must follow, when we are forced too late into the inevitable choice: to remain and diminish on an unhappy world; or to expand into the only dimension remaining perpendicularly outward from the surface into space. Then some day we may become a Type-II civilization, mastering the resources of an entire solar system. Our species cannot continue as we have on this planet for another 100 years. Doubtless it falls on us today, the very time we intended to start building a starship, to make the late choice. We wished this century to be filled with enlightenment and adventure; it could be an age of desperation and war. What a time to begin an audacious project in space! How will we maintain consistent funding for the next 100 years? Fortunately, saving a civilization, mastering a solar system, and doing other great things like building starships amount to mostly the same set of tasks. Recognizing what we must be about during the next 100 years will make it possible to do them all.

He presents a stark choice and though it’s based an arguably finite resource base, the road to freedom surely lies with not being restricted to one planet.

Metzger, Mueller and their NASA colleagues have submitted a technical paper to the “Journal of Aerospace Engineering”:

Affordable, Rapid Bootstrapping of Space Industry and Solar System Civilization

Abstract:

Advances in robotics and additive manufacturing have become game?changing for the prospects of space industry. It has become feasible to bootstrap a self-sustaining, self-expanding industry at reasonably low cost. Simple modeling was developed to identify the main parameters of successful bootstrapping. This indicates that bootstrapping can be achieved with as little as 12 metric tons (MT) landed on the Moon during a period of about 20 years. The equipment will be teleoperated and then transitioned to full autonomy so the industry can spread to the asteroid belt and beyond. The strategy begins with a sub-replicating system and evolves it toward full self-sustainability (full closure) via an in situ technology spiral. The industry grows exponentially due to the free real estate, energy, and material resources of space. The mass of industrial assets at the end of bootstrapping will be 156 MT with 60 humanoid robots, or as high as 40,000 MT with as many as 100,000 humanoid robots if faster manufacturing is supported by launching a total of 41 MT to the Moon. Within another few decades with no further investment, it can have millions of times the industrial capacity of the United States. Modeling over wide parameter ranges indicates this is reasonable, but further analysis is needed. This industry promises to revolutionize the human condition.

Robert Mueller presented on the Plan at several different meetings, his presentation slides being available here:

Robotic, Self-Sustaining Architecture to Utilize Resources and Enable Human Expansion Throughout the Solar System

I got in touch with Phil and will hopefully have more to discuss in Part II of this blog post.

An Imploding Cosmos?

A pre-print from yesterday, submitted by Branislav Vlahovic:

Observed Cosmological Redshifts Support Contracting Accelerating Universe

Vlahovic, a Professor at NCCU, discusses the possibility that our Universe is Closed and has already passed its maximum radius, at 15 billion years of age. He explains that the observed red-shift would be observed even in a collapsing space-time and the Universe might be ~24 billion years old, with 6 billion years before re-collapse in an Anti-Big-Bang. The reverse of the Big Bang, typically called a “Big Crunch”, is when all the (negative) gravitational potential energy of the Cosmos will be returned to (positive) heat energy and the contents reduced to “pure-energy”. Not healthy for Intelligent Life like us.

To have a present day Hubble parameter of ~70 km/s/Mpc the Universe would need to have a mass-energy density about 4.4 times the critical density, Omega-Naught. That means a Cosmic census of about 50 billion Galaxies as massive as the Milky-Way and a Universe that’s presently 7.5 billion light-years hyper-radius, with the opposite side some ~11.8 billion light-years away. An interesting consequence of such a claustrophobic cosmos is that we might be seeing double images of quasars – one image being their hyper-luminous form billions of years before their current more sedate Galaxy form. If peculiar velocities (non-cosmological motions) off-set the most recent image from the position of their past form, then we’ll see a Quasar with a high red-shift near a “closer” Galaxy with a lower red-shift. This would answer the puzzle of why some Quasars appear to be springing from regular Galaxies.

This web-site isn’t afraid of exploring impending Cosmic Dooms – a Sudden Singularity a few million years from now has been discussed previously – but this one is interesting. It’s not far enough away for the Cosmos to be reconfigured for a controlled collapse, as per the Omega Point Theory, but it does invite exploring ways to break-out of our Cosmos. One option, also mentioned here, is to learn how to live in black-holes, which – if sufficiently large – can survive a Big-Crunch to spring-forth in the next Big-Bang. Alternatively we might learn how to harness the worm-hole created by the Ring-Singularity of rotating black-holes – in theory this will allow access to other Universes.

Can we survive the transition to other Universes, potentially with totally different laws?