Monday, February 1, 2016

Interorbital Exchange - part 3, Mars crew

Continuing the theme, here is a look at how to transport human crew to and from Mars.

The Hohmann transfer orbit requires the least fuel but takes a long time. In order to minimize radiation exposure and overall risk, 180 days or less is the preferred travel time. Getting to Mars faster than the minimum energy path requires a lot more fuel. Accelerating a heavy habitat and its systems to high speed is expensive, but there is a solution. A special set of orbits allow us to boost the habitat up to speed one time and have that vessel pass by Mars and the Earth on a schedule, with only minor course corrections.
 These are called cycler orbits, popularized by Dr. Buzz Aldrin. A permanent habitat is built and launched into the chosen cycler orbit. This habitat will merrily roll around the solar system with periodic close visits to Earth and Mars. While much of its time is spent far away from anything useful, each cycler orbit has a 'short leg', a portion of its trajectory that passes one planet and then the other after a short time. The idea is that you only need to burn fuel for the habitat once; after that new crews and their food can be boosted to the cycler as it rolls by on future transit opportunities.

Summary: I've continued my Mars example to its conclusion of a bit under $18 billion for three manned missions (6 crew each) and about $3.1 billion for each additional trip (crew of 6, 12, 12, 18, 18, etc.).
The transit habitats implemented as cyclers offer an opportunity to to ISS-style science for about $53 million per crewmember-year during buildup and less than $10 million per year steady-state. Total program cost would be about $22.5 billion, including $6.25 billion covered under the Mars program.

Full details after the break.

 Not all cycler orbits are free (read: ballistic). Some require periodic burns to stay in sync with the ~15-year Earth-Mars cycle. We want to use orbits that require no major burns, only minor stationkeeping (less than 100m/s per year).

 To dig directly into heavy details, here is a paper  (Landau, Longuski, Aldrin 2007) on the subject of Earth-Mars cyclers and their properties. That paper references a particular cycler orbit (McConaghy, Yam, Landau, Longuski 2003) called S1L1 that requires no deep-space maneuvers (that is, requires no fuel) and maintains its alignment using only gravity assists. In addition, the dV requirements to taxi to and from the habitat are fairly modest. The downside is that there are two of this orbit, one with a short leg from Earth to Mars and one with the short leg from Mars to Earth. Another downside is that the orbit repeats every two synodic periods, so if we need departure and return habitats every period then we need four habitats.
  Each cycler passes close to Earth twice for each trip to Mars, and each has one short leg (110-220 days), one medium leg (530-550 days, always the Earth to Earth leg) and one long leg (790-940 days, much of it beyond the orbit of Mars). The wide range of travel times are because of the relative positions of Earth and Mars during the 30-year repeating cycle; these values are from the authors' calculations using ephemeris for 2005 through 2040. Each round trip takes two synodic periods, or 1,560 days (4.27 years) in total.
 The Mars approach occurs with Vinf of 5km/s. Mars escape velocity is also 5km/s, so the hyperbolic velocity is 7.07km/s. Orbital speed at a 300km orbit is 3.55km/s so the required dV is 7.07 - 3.55 = 3.52km/s. My cargo tug would need about 6.8t of fuel for the return burn and could deliver something like 38 tons to the cycler from low Mars orbit.
 The Earth approach has a Vinf of 4.7km/s each time.  Earth escape velocity is 11.53km/s, so the hyperbolic velocity is 12.45km/s. Orbital speed at a 400km orbit is 7.67km/s so the required dV is 4.78km/s. But wait... we're not launching from LEO, we're launching from EML1. We nudge into an elliptical orbit of 6778x326,380km (periapsis 400km above Earth's surface) with semi-major axis of 166,600km and periapsis speed of 10.73km/s. The dV required is now 1.72km/s plus the 0.77km/s to leave EML1, a total of 2.49km/s. My cargo tug would need 4.2 tons of fuel for the return burn and could deliver 70 tons of cargo to the cycler.

 So, we've established that the basic exchange infrastructure can be used to transfer cargo to and from cycler orbits. Each cycler can receive one shipment at Mars and two shipments at Earth every two periods, totaling 178 tons at the most with a single cargo tug. Every period, one crew ships out to Mars and one crew ships back to Earth, each taking the short leg of their respective cyclers.
 One might ask why we would ship so much cargo to a cycler when the mission cargo is traveling by Hohmann transfer. Radiation is the answer. Shielding against radiation requires a lot of heavy armor. Instead of shipping this mass from Earth, we use water and refinery slag from the Moon and Mars / Phobos. On the Mars end, a lot of the non-shielding cargo is nitrogen for fertilizer and buffer gas plus argon for ion fuel. On the Earth end we ship any required spares and additional hardware for expansion. The first trip in each cycler is about as risky as the baseline NASA transit habitat, but each successive trip has more shielding and more habitable volume for a safer journey.
 A key element of the cycler habitat is that it is large enough to provide spin gravity, with one or more transhab-style modules on a long tension truss opposite the main power systems and additional cargo. This environment is suitable for long-term human habitation. In fact, the medium leg trip (Earth to Earth, ~540 days) could be used much like the ISS is used today, as a platform for space science but with access to heliocentric space down to about 0.8 AU. If the cyclers are inhabited for the long leg as well then they will also reach beyond the orbit of Mars, offering opportunities to observe the main belt from within the inner edge.

 Cost is a driving factor. I'm estimating that each habitat module is similar to (or composed of) a BA-330 habitat at about $250 million each. Two can be launched on a Falcon Heavy for $150 million and each cycler requires a minimum of two. The cyclers will require a significant amount of power to run hydroponics and will need to perform beyond Mars orbit. As a baseline, let's assume that the balance of structure and systems is 30 tons at $15 million per ton ($450 million), with a second FH launch also at $150 million. Now we're at $1.25 billion per habitat or $5 billion for the program. That may sound expensive, but consider that the ISS has cost about $150 billion and provides only 916m³ of habitable space, while each cycler will provide 660m³ and the program will provide 2,640m³ of space.
 Further expansion would be to add a habitat module and additional system hardware totaling 35 tons and $625 million at each period for each cycler. By the time the first habitat module pair has reached its 30-year design life the cycler will have 9 modules, stabilizing to 7 active modules within design life and 2,310m³ of habitable volume. This is just over ten times the volume of the ISS for the cycler fleet. Accumulated radiation shielding has no expiration date and can be used indefinitely. Over the first 33 years of the program, the cyclers will cost $22.5 billion. At that point they can be operated steady-state, with seven modules active and all older modules operated as contingency facilities, used as shielding or returned to EML1 for refit. The long-term maintenance would run about $590 million per year with facilities for 84 permanent occupants, twice that if at least half of the food is shipped in from other sources. The buildup phase would provide 422 crew-years (assuming the first flight of each cycler is short trip crew only) at a cost of about $53 million per crew-year in facilities. Crew launch costs, food and other consumable supplies are not included in that cost, but even if costs were equal to the cost of facilities it would still be less than $300k per person-day. Ongoing operations would cost $7 million per crew-year (less than $20k per crew day), again not including food, consumables and crew launch costs.

 With the three parts of a Mars mission outlined we can see what the overall cost would look like using ISRU and reusable infrastructure. It looks like a set of three missions would require $6.25 billion in transit habitat costs and $11.4 billion in cargo operations (with ISRU included). $17.65 billion spent over 8.5 years of operation (one period of ISRU startup, 3 periods of manned missions) and perhaps 3.5 years of design works out to an average of about $1.5 billion per year. Most other baselines show funding levels several times that amount. I'd like to point out that this architecture would also result in tens of tons of samples returned to Earth and would reduce the per-mission cost of future missions to  $3.1 billion per trip while increasing the crew sizes to 12 or more; this is about the same intensity of $1.5 billion per year with increasing science return over time.

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