32 thoughts on “My Mars Spreadsheet”

1. Astonishing is in the eye of the beholder, this has been known for years. I’m surprised you’re surprised.

   The delta-v difference looks suspicious though, the additional circularisation and the additional orbit raising farther away from the sun should be more expensive. A quick inspection of your spreadsheet suggests that you’re not counting the delta-v from LEO to L1/L2 in the total. The difference underlines how useful cycling a heavy MTV between Earth and Mars Lagrange points would be compared to cycling between low orbits, but you still need to count the transfer from low to high orbits and vice versa appropriately.

   I’ll wait for your corrections, but one thing I noticed was that on the first sheet cell B61 is defined as B61 = – B36 / B31, but it should be – B35 / B31. Not that it makes much of a difference, since the numerical values are close.

   1. OK, I missed that cell, and just uploaded a new version with that fix. All of the errors were of that nature, where I had a radius in the numerator rather than the gravitational parameter for that body.

   2. I was astonished at the magnitude of the benefit, and it turns out that I was right to have been. Factors of three and five are more intuitively satisfying than ten and twenty.

      1. I see. Nevertheless the advantage of using Lagrange points as staging orbits is surprisingly large. Never underestimate the power of a fully fueled Centaur at L1/L2. As a corollary, don’t overestimate the need for an RS-68, J-2X would be massive overkill already. We can get 15mT chunks to L1/L2 with existing stages, which is enough. Imagine how large a stage you could fit inside an EELV fairing and within 15mT dry mass. Get it to L1/L2 and refuel it there, which can be done in almost arbitrarily small packets. Then compare the power of that monster to the already enormous power of Centaur. I don’t think we’ll ever need an HLV, unless it is to launch hundreds of people into space at once or something like that.

2. Also see http://en.wikipedia.org/wiki/Delta-v_budget#Delta-vs_between_Earth.2C_Moon_and_Mars

   Exercise for the reader: calculate which would have more of an effect on IMLEO, using SEP combined with hypergolics or all-chemical LOX/LH2.

   Further exercises:

   – discuss which is more important, IMLEO * specific launch costs or just IMLEO.
   – discuss which is more likely to lead to a propellant launch market soon (and thus funding for cheap lift, which to first order is the only thing that matters)

   😉

   1. I infer from your second question that you think that demanding more propellant in orbit due to lower Isp is better because it will drive down launch costs further?

      My thinking is that I’d like to establish an infrastructure that doesn’t have to deal with nasty acids and can be easily produced from in-situ resources, and that even with the more efficient propulsion, there will be adequate market for launch, assuming there’s any market for significant beyond-LEO missions.

      1. Hypergols are not necessarily nasty acids. See http://en.wikipedia.org/wiki/HPGP for example.

         1. Second..

            One great storable propellant is RP-1.

            H2O2 is incredibly underrated as an in-space oxidant.

            I yield to no-one in my enthusiasm for new technology in space and am trying to get through to SLS advocates that it was the technology development program that suffered most from their irrational lust for a BFR.. but we don’t *need* technology development to go to Mars with existing boosters. We don’t *need* low boiloff cryogenic depots. They are *nice to have* but they come later. Just fly already.

            1. Well, take the spreadsheet and run your own numbers with alternate propellants. I personally don’t think that cryos are that big a deal, technologically. Especially in deep space, where all you need to keep them cold is a sun parasol.

            2. At this point I don’t fully understand your spreadsheet so I’m probably making a silly mistake, but…

               If I change the ISP from 470 to 300 the improvement goes up about seven times. Is that right? (That would be with vs without refueling… not 470 vs. 300)

            3. If I change the ISP from 470 to 300 the improvement goes up about seven times. Is that right?

               Probably, though in theory you should also adjust the stage fraction somewhat to account for the higher propellant density.

      2. Not really, I think the lower Isp is a price that’s worth paying, but it’s not an advantage. The argument is time preference and lower risk, a greater risk-adjusted NPV of launch revenues, and therefore a better business case for RLVs.

         I agree about the nasty chemicals and ISRU, but if chosen well, a program that starts with a refuelable hypergolic spacecraft can be totally agnostic as to the propellant type, number, location and date of deployment of depots, whether to use SEP and on which segments, whether to use aerobraking, ISRU, NTR, (commercial) HLVs etc etc. Over time I would expect it to bring online most of those technologies, at the economically responsible moment. The alternative seems to be to let civil servants make at least some of those decisions.

   2. http://clowder.net/hop/railroad/deltaveemap.html

      1. Thanks for the link. Lot of cool stuff to read there.

3. Mmeijeri Suggested in comments to your last post that a powered Earth flyby would be better. Dropping from high lunar orbit to a close Earth flyby with propulsive burn at perigee should require less than a kilometer per second of power for a TMI using the Oberth effect. Unless i am misunderstanding your points, a depot in high lunar orbit would be considerably more efficient than an interplanetary one.

   1. John, I’m proposing both, though my analysis didn’t consider the close-earth flyby. That would be yet another refinement that would improve the performance at little cost in time. It would apply to both of the EML1 scenarios. Martijn is welcome to update the spreadsheet accordingly. I think I’ve already taken the ball about 90 yards down the field — he can go in for the touchdown (even if he doesn’t understand the metaphor)… 😉

      1. I was thinking in terms of using the lunar orbital velocity to counter the Earth relative velocity at the depot distance. From L1 it would take several hundred meters per second to slow down to hit the Earth flyby, while it would take considerably less with a proper burn from high lunar orbit. In the cases we are discussing, every mps counts.

      2. Heh, I’m the opposite of an athlete, but I think I do get the metaphor. It might not be wise for me to start fiddling with your spreadsheet however, since I have a monster spreadsheet of my own that keeps growing and growing, although I haven’t had much time to work on it lately. I have a basic Lambert solver capable of making delta-t vs delta-v calculations (and eventually porkchop plots), but I got stuck analysing the intricacies of plane changes when life intervened and I had to go make some money. Maybe we can combine some calculations eventually.

         But the strategically important part is the delta-v chart, which you can get off Wikipedia. It’s fun to be able to do the delta-v calculations yourself, and I recommend it to anyone with a strong mathematical background, but the chart itself is enough for rocket equation level analysis, which should be in reach of anyone with high school mathematics and basic knowledge of Excel.

         It shows you that as long as you have refueling, you don’t need large transfer stages or launch vehicles, you don’t need anything bigger than an RL-10, wider than an EELV fairing, larger capsules than Dragon etc etc. This is true even with hypergolics. The chart also shows the benefits of cyclic between edges of gravity wells instead of bottoms of gravity wells and the benefits of high Isp propulsion such as SEP.

4. You gentlemen are talking SO for over my head here, that I’ll just wait for the “Gas Stations to Mars, Special”, on the Discovery Channel. Maybe Mike Rowe can explain it to me.
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   Rand, I think this next, is so true that it’s scary.
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   …this is an excellent example of a need to have a feel for the numbers, and not just trust what comes out of a computer (as I fear too many young people do these days)
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   I’ve had a number of conversations with family and friends about FACT Checking stuff they are sent or that they find online. I was really shocked a couple of times at the number of people, whom I thought were smart, who sent my some of the internet blurbs about Obama being the love child of Hitler and Idi Amin’s mother! OK, that is an exaggeration, but not by much.

   I don’t know if everyone has seen it, but one of the insurance companies is running a commercial, where an insurance adjustor and a female friend are talking. He tells her he’s running numbers or completing a report on his special app (that ONLY his company has), and how easy, quick and great it makes his company.

   She says something to the effect that SHED read that the app didn’t really work…

   …where’d you read that?, says he.

   …on the internet?

   …and you believed it?, he asks.

   …well, yeah. They can’t put anything on the internet that isn’t true.

   …where’d you read that?, he asks.

   …ON the internet! [they both say in unison ]

   It’s so insane that so many people believe that everything on the internet is true, that someone on Madison Avenue picked up on it and made fun of their idiocy on a commercial. And I thought I just knew a bunch of stupid people!

5. 365.25 days in a year? B68, 70, 71

   1. In the context of this analysis, that sort of precision is unnecessary.

6. I really wish somebody would bring back a program like the old Microsoft Space Simulator. I used to amuse myself for hours by calculating orbital translations and Mars rendezvous by hand and then seeing if they would work in the simulator. (I’m kinda weird.)

   This looks kind of promising, in a more game-ish sort of way…

   http://kerbalspaceprogram.com/

   1. If you’re on the PC, try Orbiter.

      http://orbit.medphys.ucl.ac.uk/

7. Rand – Have you read the analysis of fuel depots done at JSC by the Safety & Mission Assurance group? (It was mentioned on NASA Watch a few months ago.)

   It pretty well lays out a case as to why a propellant depot system is a good idea for mission reliability. The key is to not require “n” missions to fill up the depot, but “n of m”. If you choose the latter, you can make the propellant delivery more reliable than the launch of the vehicle that needs refueling. They recommended commercially contracting with a minimum of two propellant providers to mitigate the risk of one source of supply, and it was seen as a good way to support the commercial launch market.

   1. Yes, I used that as a basis for a talk on depots I gave at JPL a few months ago.

8. Its nice to see3 there is still a bit of the old Rand left 🙂

9. I really don’t think you want to put a depot in heliocentric orbit like that, and particularly not a circular heliocentric orbit. Even if it gives an optimal delta-V breakdown, the phasing considerations are going to be impossible for anything that has to break even in less than decades. Better to accept off-nominal performance with better operational characteristics.

   Something like an Aldrin cycler might work, but I’m seeing good results using just depots at the Earth-Moon L2 and Sun-Mars L1 points. The delta-V split for a trip to Phobos comes to:

   3.4 km/s LEO to E-M L2
   2.1 km/s E-M L2 to M-S L1
   0.95 km/s M-S L1 to Phobos

   vs.

   5.8 km/s LEO to Phobos direct

   All patched-conic impulsive burn trajectories with Oberth departure and capture burns but no aerobraking. Assuming a Centauroid space tug with 450 seconds Isp and an 0.85 bus propellant fraction, I get:

   5.23 kg propellant per kg payload for LEO->Phobos direct, vs
   2.53 kg propellant per kg payload using the dual depots.

   That’s close to 50% savings with no major phasing considerations; you get a launch window every 2.15 years just like always.

   There’s also the question of how you get the payload to the depots. The math is a bit hairier on that one, but accounting for a round-trip tanker service to the depots I get, using chemical rockets only:

   10.27 kg propellant/payload if all propellant is sourced in LEO
   5.63 kg propellant/payload if we have a Lunar surface fuel plant
   3.52 kg propellant/payload if we have both Lunar and Phobos ISRU

   And if we can use ion- or plasma-drive tankers (2500s Isp but only 70% propellant mass fraction):

   3.76 kg propellant/payload if all propellant is sourced in LEO
   2.76 kg propellant/payload if we have a Lunar surface fuel plant
   2.70 kg propellant/payload if we have both Lunar and Phobos ISRU

   So, it’s a net win with either EP tankers or in-situ propellant use, and a huge win with both.

   1. How are you getting lower delta-v through use of staging orbits? After all, you are doing additional circularisation and perigee lowering burns.

      I thought Rand was talking about the benefits of splitting the journey into several legs, each using the most appropriate form of propulsion for that leg and the cargo it is carrying. That shouldn’t save delta-v, but it could allow higher overall Isp.

      To that we can add the benefit of cycling between high energy planetary orbits instead of using a heliocentric staging orbit in the case of reusable MTVs, which would actually save delta-v, regardless of Isp.

      But aside from cycling, surely end-to-end delta-v (though not mass ratio) must be higher if you using multiple staging orbits? Assuming you’re not using something like the Interplanetary Transport Network.

      1. Total delta-V is higher. 3.4 + 2.1 + 0.95 = 6.45 km/s to Phobos via depots, compared to 5.8 km/s direct. So you lose 650 m/s to, essentially, circularization and perigee lowering – at very high “altitude”, where the cost of such things is low.

         And you don’t need to change propulsion types to capture the benefits of this strategy. A single vehicle with a single propulsion system, as I described, can be half the size and burn half the propellant, because it can be sized for 3.4 km/s rather than 5.8 km/s. Smaller tanks, smaller engines, and with that less structure, thermal, RCS, etc, hardware. And when you do that 3.4 km/s burn at the start, you aren’t wasting fuel hauling the propellant you will use for the remaining 3.05 km/s; it will be waiting for you when you get there.

         Delivered, hopefully, by either from a more convenient location than LEO or by a more efficient tanker than your chemical-rocket manned Mars ship.

         Using multiple propulsion systems for the Earth/Mars trip itself can give further gains, but that’s material for a technical paper, not a blog post.

         1. I see, I misunderstood your point. The ability to use smaller vehicles, with less constraints on thrust, Isp and mass ratio is indeed very important by itself. And even present technology allows for prepositioning of storable propellant to EML1/2, SML1/2 and LMO.

            And high energy staging orbits also suffer less from boil-off and phasing problems.

10. Thanks alpha nerds.

11. Another interesting fact is that with propellant depots you can have a single vehicle, that is a single stage, that travels, all to Earth orbit, the Moon, and to Mars:

    The Coming SSTO’s: Applications to interplanetary flight.
    http://exoscientist.blogspot.com/2012/08/the-coming-sstos-applications-to.html

    Bob Clark

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