Thanks very much for posting this! I have a question about the early part of your presentation, where you discuss the characteristic energy of various trajectories. It looks like your treatment includes only the gravitational potential due to the mass of the Earth. Is that realistic for Earth-Moon Lagrange points? What about the mutual potential energy of the object and the Moon?

I like EML 1 or 2 in regards to getting crew fast to Mars.

Due to EML2's proximity to the moon, I'm putting this in the moon section. I hope to expand on this as I have time.Pellets in pic above are all nudged from EML2 with tiny burns varying by meters/sec. The blue pellets sail into heliocentric orbit.Check out the #3 orange pellet -- it has a perigee deep in earth's gravity well. Using the sun to lower perigee, we can go from EML2 to a deep earth perigee with less than a .1 km/s nudge. An 6678 x 180000 ellipse has perigee velocity of 10.9 km/s. At this speed a .4 km/s suffices to send the pellet into an 11.3 km/s hyperbolic orbit for Trans Mars Insertion.

The orange trajectory is about 100 days, right?

Let's imagine Impaler's MTV -- a 200 tonne Mars Transfer Vehicle (MTV) propelled by Hall Thrusters with acceleration of .000001 km/s^2. 11.6 days of acceleration gets 1 km/s delta V. It takes this ship about 3 months to spiral out of earth's gravity well. We don't want humans aboard, especially during the ~2 month spiral through the Van Allen Belts. It makes sense to send humans to dock with the MTV after it's climbed most the way out of earth's gravity well.

Radius of the MTV's spiral will eventually reach 327,000 km, the distance to the moon's Hill Sphere. So why not let the MTV spiral to EML1 and let the moon lend a hand getting the MTV to EML2? Park the MTV at EML2 where station keeping is inexpensive.Send humans to EML2 to rendezvous with the MTV. From LEO to EML2 is 9 days and about 3.5 km/s.As pictured in the OP, EML2 is pretty close to C3=0. But at a speed of 1.15 km/s, it doesn't enjoy much Oberth benefit. The MTV still needs to do another 3 km/s to reach a 1.52 aphelion (Mars' distance from the sun). At 1 km/s per 11.6 days, it will need about 34 days to achieve this 3 km/s.Now let's imagine there's propellent and life support consumables at EML2. These might come from lunar cold traps or asteroids parked in a DROs. Stocking the MTV with EML2 water (for drinking, sanitation and radiation shielding) and EML2 oxygen to breathe would substantially reduce the gross lift off weight from earth's surface.The MTV docks with a reusable Earth Departure Stage (EDS). This stage has a dry mass of 31 tonnes and carries 76 tonnes of lox/methane. At 107 tonnes the EDS is a little more than half the MTV's mass. Total mass at EML2 is now 307 tonnes.EML2 to TMI is about .9 km/s and exhaust velocity of lox/methane is 3.6 km/s. e^{(.9/3.6)} - 1 is .28. So getting this 307 tonne mass to TMI will take 68 tonnes of prop.After TMI, the EDS separates from the MTV. It still carries about 9 tonnes of lox/methane. A .5 km/s braking burn slows it to an elliptical orbit with an apogee of about 1 lunar distance. After about 5 orbits the apogee nears the moon. At perilune .18 km/s injects it into a elliptical lunar orbit with apolune near EML2. At apolune .14 km/s parks it at EML2.ELM2 to TMI is 9 days. TMI to the edge of the Hill Sphere is about 6 days. 34 - 15 = 19. 19 days isn't much of a savings but this is the outbound trip.

If I remember right, Impaler's MTV is reusable and returns to earth. Does it spiral back down to LEO? This would add another 7 km/s to it's delta V budget and 3 months to trip time. With the infrastructure I'm talking about it would only need to spiral to EML2 and then chemical rockets could take the astronauts from EML2 to LEO. To refuel the MTV, xenon would have to be delivered to EML2. But a xenon delivery tanker would be a small fraction of the mass of the MTV.Impaler's MTV would be good for moving between heliocentric orbits but would suck at descending/ascending planetary gravity wells in a timely manner. It'd be well suited for traveling between EML2 and Deimos.But I consider Mars colonization an unlikely fantasy if building space infra-structure gives no return on investment. Far more plausible in the near term is an asteroid retrieval vehicle as suggested in the Keck Report. At least Planetary Resources has a shot at enjoying ROI.The Keck vehicles would take nearly two years to spiral from LEO to C3=0. For these more plausible vehicles the time savings could be huge.

I've made a spreadsheet of Non-Hohmann transfers. Time can be shortened by shrinking the transfer ellipse's perihelion (which needs to be less than 1) or increasing transfer ellipse's aphelion (which needs to be more than 1.524).Attached is a screen capture from a spread sheet where the Earth Departure Stage would do a 3.1 km/s perigee burn. Since falling from EML2 takes .4 km/s, the EDS would need a total delta V budget of about 3.5 km/s. This wouldn't be a reusable EDS.Coming to Mars, a 4.67 km/s peri-aerion burn would capture the MTV into a 3697x23459 km ellipse. This is atmosphere grazing with apo-aerion at Deimos height. Orbital period is 13 hours, so about 2 periaerion drag passes per day. More drag passes per day as apo-aerion is lowered. I believe aerobraking could circularize the orbit within a week or so.This transfer would take 3.4 months or about 103 days. I've also attached the spreadsheet. A user can play with the transfer orbit by changing aphelion and perihelion.

Departure orbit radius 1 A.U. Speed 6.283185307 A.U./yr Destination orbit radius 1.524 A.U. Speed 5.089643749 A.U./yr 4.740604351 AU/yr to km/sTransfer orbit perihelion 0.7 A.U. Transfer orbit aphelion 1.53 A.U. 2r1 2Flight path angle at departure 0.36777381 Radians 21.07188715 degrees Perigee burn (300 km altitude falling from high apogee) Vinfinity at departure 2.375992013 A.U./yr 11.26363808 km/s 4.888082825 km/s Flight path angle at destination 0.067838707 Radians 3.88687157 degrees Periaerion burn to a 3697x23459 km ellipse Vinfinity at destination 1.084314564 A.U./yr 5.140306341 km/s 2.568080059 Time of Flight 0.370249764 years 4.442997163 months 135.2337261 days

Transfer orbit perihelion 0.87 A.U. Transfer orbit aphelion 1.524 A.U. 2r1 2Flight path angle at departure 0.222899017 Radians 12.77117293 degrees Perigee burn (300 km altitude falling from high apogee) Vinfinity at departure 1.534703827 A.U./yr 7.275423642 km/s 2.321668688 km/s Flight path angle at destination 0 Radians 0 degrees Periaerion burn to a 3697x23459 km ellipse Vinfinity at destination 0.750540983 A.U./yr 3.55801785 km/s 1.511760053

For the earth flyby, you would get at least some oberth effect for the part of the acceleration done in the earth gravity well.

Quote from: Hop_David on 05/09/2015 09:25 AMI've made a spreadsheet of Non-Hohmann transfers. Time can be shortened by shrinking the transfer ellipse's perihelion (which needs to be less than 1) or increasing transfer ellipse's aphelion (which needs to be more than 1.524).Attached is a screen capture from a spread sheet where the Earth Departure Stage would do a 3.1 km/s perigee burn. Since falling from EML2 takes .4 km/s, the EDS would need a total delta V budget of about 3.5 km/s. This wouldn't be a reusable EDS.Coming to Mars, a 4.67 km/s peri-aerion burn would capture the MTV into a 3697x23459 km ellipse. This is atmosphere grazing with apo-aerion at Deimos height. Orbital period is 13 hours, so about 2 periaerion drag passes per day. More drag passes per day as apo-aerion is lowered. I believe aerobraking could circularize the orbit within a week or so.This transfer would take 3.4 months or about 103 days. I've also attached the spreadsheet. A user can play with the transfer orbit by changing aphelion and perihelion.QuoteDeparture orbit radius 1 A.U. Speed 6.283185307 A.U./yr Destination orbit radius 1.524 A.U. Speed 5.089643749 A.U./yr 4.740604351 AU/yr to km/sTransfer orbit perihelion 0.7 A.U. Transfer orbit aphelion 1.53 A.U. 2r1 2Flight path angle at departure 0.36777381 Radians 21.07188715 degrees Perigee burn (300 km altitude falling from high apogee) Vinfinity at departure 2.375992013 A.U./yr 11.26363808 km/s 4.888082825 km/s Flight path angle at destination 0.067838707 Radians 3.88687157 degrees Periaerion burn to a 3697x23459 km ellipse Vinfinity at destination 1.084314564 A.U./yr 5.140306341 km/s 2.568080059 Time of Flight 0.370249764 years 4.442997163 months 135.2337261 days This appears to have flight time of 4.44 month, but I would guess that's it's at top of the perihelion orbit, and so one would do a patched conic, like you do with most Hohmann transfer to mars and thereby shorten the travel time, plus that would be adding some orbital speed so one is going closer to Mars velocity [mostly regarding it's orbital vector].Anyways it's less delta-v than I expected. And I think minimum travel time should be 3 months for crew.Edit: I mean from the crew launching from Earth it should take 3 month or less to reach Mars [Though could be less travel time but would take considerable more rocket fuel and it seem with enough shielding 3 months should fast enough so reduce microgravity effect and crew radiation exposure].

Admittedly hydrocarbons are far easier to store so perhaps this is your motivation,

but if the source is the lunar cold-traps then presumably hydrogen can be stored their passively with zero boil-off and the propellent delivery could be done via a 'launch on demand' directly to the waiting vehicle at EML2.

Finally the dry mass of the stage seems rather high, you said this stage is intended only for use in space so it should be free of most parasitic mass other then insulation to keep boil off to a reasonable level during the ~2 weeks in which it actively has propellent, I would think that 10% dry mass would be a perfectly reasonable figure, unless their are other demands being put on it that I don't know of.

I suspect that a simple increase in the propellent tank for the MTV will be able to fully replace the EDS. At 3000s the MTV would need 10% propellent fraction to do 3 km/s. Thus our 200 ton vehicle could just be 220 tons at EML2. Now more propellent at LEO would be needed for it to push that larger mass up to EML2, as the DeltaV from LEO to EML2 is 7 km/s for low thrust vehicles that means a an additional 20% on top of the additional propellent to get the additional propellent to EML2, which is 5 tons. So in totality the MTV needs 25 tons more IMLEO in propellent (Xenon) to replace the EDS.

And while I think the EDS presented above is too conservative and could be considerably lighter it will not be so light as to cost competitive with a simple enlargement of the MTV tanks, to speak nothing of the infrastructure costs of establishing in space propellent production.

That's a really neat class of trajectories! Does your pellet simulation tell you the end state of the pellets (i.e. position and velocity), so you could calculate their specific orbital energies to see if they are greater than zero?

Unless the ULA propellent depot boys (Zegler, Kutter, & Barr) manage to reduce boil off. I give them better than even odds if they are funded. But perhaps I'm succumbing to the space cadet optimism I'm prone to.

As mentioned, infra structure capable of making propellent could also provide water and oxygen. Drinking water, water for cleaning, radiation shielding, and oxygen to breathe could make up nearly half an MTV's mass. So 125 tonnes more in IMLEO.

I don't expect reusable upper stages. I do believe Musk will be able to re-use boosters but there will be refurbishment and transportation costs.If earth is the sole source of propellent, I expect Musk to cut launch costs by half, but not more than that.

Let's imagine Impaler's MTV -- [...] with acceleration of .000001 km/s^2. 11.6 days of acceleration gets 1 km/s delta V. It takes this ship about 3 months to spiral out of earth's gravity well. [...]Radius of the MTV's spiral will eventually reach 327,000 km, the distance to the moon's Hill Sphere.

Quote from: Hop_David on 05/09/2015 08:00 AMLet's imagine Impaler's MTV -- [...] with acceleration of .000001 km/s^2. 11.6 days of acceleration gets 1 km/s delta V. It takes this ship about 3 months to spiral out of earth's gravity well. [...]Radius of the MTV's spiral will eventually reach 327,000 km, the distance to the moon's Hill Sphere.I'd like to contribute to this thread a (still incomplete) analysis of the spiral out from LEO to the cislunar vicinity. (Long term I would like to be using something open source, but the free Mathematica for Raspberry Pi was sufficiently tempting.) Taking a hint from a discussion related to this on stackexchange I use a state vector of (r, v, gamma, phi} to make the acceleration in the direction of the velocity vector easy. The results below start from 400x400 km LEO and use the 0.001 m/s^2 constant acceleration mentioned above. After 77 days the spacecraft has completed more than 345 revolutions around the Earth, reached an altitude of 323,657 km and a velocity of 1233.58 m/s. (The semi-major axis of the resulting orbit is 446,048 km, which certainly gets it within the Moon's Hill Sphere.)

Quote from: Hop_David on 05/09/2015 08:00 AMLet's imagine Impaler's MTV -- [...] with acceleration of .000001 km/s^2. 11.6 days of acceleration gets 1 km/s delta V. It takes this ship about 3 months to spiral out of earth's gravity well. [...]Radius of the MTV's spiral will eventually reach 327,000 km, the distance to the moon's Hill Sphere.I'd like to contribute to this thread a (still incomplete) analysis of the spiral out from LEO to the cislunar vicinity. (Long term I would like to be using something open source, but the free Mathematica for Raspberry Pi was sufficiently tempting.) Taking a hint from a discussion related to this on stackexchange I use a state vector of (r, v, gamma, phi} to make the acceleration in the direction of the velocity vector easy. The results below start from 400x400 km LEO and use the 0.001 m/s^2 constant acceleration mentioned above. After 77 days the spacecraft has completed more than 345 revolutions around the Earth, reached an altitude of 323,657 km and a velocity of 1233.58 m/s. (The semi-major axis of the resulting orbit is 446,048 km, which certainly gets it within the Moon's Hill Sphere.)[EDIT: 75 days is apparently enough. Added below is a revised trajectory showing 75 days of propulsion spiral and the resulting orbit, and also the (average) orbit of the Moon.]

There's a free version of Mathematica?