What are the Odds?

I wanted to expand on one thought from last night. If you have a launch vehicle that you want a reasonably good chance of reusing 1000x, it actually needs a lot better than a 1:1000 Loss of Vehicle probability for any given mission. With a 1 in 1000 chance of losing the vehicle on any given flight, you actually have a very high chance of losing it long before the 1000th flight. The odds of not losing a vehicle in x consecutive flights with a given reliability rating (probability of a non-LOV flight) is:

Psurvive_all = PnoLOV ^ x

Or solving for the required probability of not losing a vehicle on any given flight (assuming an equal probability on any flight):

PnoLOV = Psurvive_all^(1/x)

So, if you want a 75% chance of surviving 1000 flights in a row, you get:

PnoLOV = 0.75^.001 = .9997 or about 1 in 3500 probability of losing the vehicle on any given mission.

If you’re ok with a 50% chance of surviving 1000 flights in a row, you need more like a 1 in 1500 probability of losing the vehicle on any given flight, and if you want a 90% chance, you’re up to almost one in 10,000.

Long story short, if you want a high probability of amortizing the vehicle over 1000 flights, you’ll need to do much, much, much better than the historical best reliability levels of liquid fueled rockets (98% or so at a 95% confidence interval). This suggests that design for survivability is likely going to be just as important as design for performance or design for cost if you want a lot of flights on an airframe.

Posted in Launch Vehicles | 12 Comments

SpaceX Mars Plans: Jon’s First Take

I’ve had a lot of friends ping me today about my thoughts on Elon’s Mars talk today. I was in a meeting when it happened, and literally was pinged by half a dozen people during the meeting… Now that I’ve had a time to chew and digest things a bit, here’s a bit of a stream of consciousness take on the plan.

Overall my feelings are mixed. I think the plan has a lot of good points, could probably work given enough money, and would likely be a better use of money than whatever NASA does for its so-called Journey to Mars, but also am really skeptical about a lot of the technical choices made, and the likelihood of hitting the price points SpaceX is predicting.

First, what I liked (some minor, some major):

  • In-Space Refueling: Elon’s plan is built around the idea of refueling his ITS (Interplanetary Transport Ship) in LEO prior to Mars departure. The BFR would have to be a lot bigger, and/or 3STO, to loft a fully-fueled ITS without LEO tanking. This is a point that ULA has been making for over a year now as well–“Distributed Lift” allows you to do a lot more with a given sized booster. As someone running a company trying to develop the rendezvous/capture and propellant transfer technologies needed for Distributed Lift, this was a welcome choice.
  • Mars ISRU: Bob Zubrin has been beating on this drum since I was a teenager, and while I think Elon’s handwaving the challenge of generating 1000s of tonnes of propellant on the Martian surface, not having to haul that all the way from Earth saves a lot of launch mass to LEO, and makes reuse of the lander a ton easier.
  • Lifting, High-Alpha Mars Entry and Supersonic Retropropulsion: By coming in sideways, and doing a somewhat lifting reentry, they’re able to bleed off enough energy early on so that the supersonic retropropulsion delta-V can stay modest even though ballistic coefficients suffer from the square cube law. If they had tried a base-first, low-lift entry, they probably would need a lot more landing propellant.
  • Reusability in General: I’ve always been a fan of both in-space and earth-to-orbit reuse. I think it’s a key to get costs anywhere close to what Elon wants.
  • Depots for Extension Beyond Mars: I also really liked Elon’s point about how his architecture can eventually include depots in various orbits, and that once you do that, you could theoretically use these vehicles for traveling almost anywhere else in the solar system you want. Many of those flights would require more radiation shielding, and possibly some level of artificial gravity to work out, but he’s totally right that once you have depots, the solar system is your oyster. Regular readers of this blog won’t find that too surprising.

Now for what I didn’t like as much (some minor some major):

  • Too Big: Something 3.5x the size of a Saturn V seems like overkill. Doing a BDB-sized launch vehicle but with near-SSTO mass ratios and the highest chamber pressure large propulsion systems to ever fly is a challenge, and I think SpaceX is likely underestimating the challenges with doing an RLV that size, and with that many engines. One thing I wonder about is if they’ve done the acoustics analysis on launching something that big. We’re talking about something several times bigger than Saturn V or Shuttle, and an order of magnitude bigger than the Falcon 9 powered landings they’ve already done. May be a non-issue, but I think both Bezos and Musk are making a mistake with how big of vehicles they’re going after.
  • Swiss-Army Knife ITS: Trying to make the ITS do so much doesn’t bode well to me for keeping it affordable. We’re talking a near-SSTO performance level reusable upper stage, who’s ascent and landing propulsion has to double as a rapid-response launch abort system, with a what amounts to a 100 person space station on top of it. Many SpaceX fans seem to think that slapping more requirements onto the most challenging piece of the overall architecture will somehow save costs compared to developing two or three more optimized system elements, but I’m really, really, really skeptical. This seems like repeating one of the dumbest mistakes from the Space Shuttle.
  • Vertical Mars Landing: I know SpaceX is sticking with what they know, but the crew and payload section on ITS looks like it’s ~30 meters off the ground level. That’s some really long ladders and/or elevators or cranes, which aren’t going to be light. Heck, ITS makes the LSAM look reasonable when it comes to payload accessibility. I know a horizontal powered landing approach ala DTAL/XEUS would require additional engines and potentially landing complexity (depending on what changes you made to the rest of the architecture), but they would probably require less mass than hauling everything down from what amounts to an 8-9 story tall building.
  • Not Refueling In Mars Orbit: I don’t have the exact EDL delta-V requirements for ITS, but it’ll probably take close to 1/3 of the Mars Orbit mass in propellant. Aerocapture/braking first into Mars orbit doesn’t really change the vehicle requirements much, it allows you to cut down on the TMI mass by 1/3. Launching ITS from the surface with only enough prop to get to Mars orbit, and then refueling in Mars orbit, can also dramatically cut down on the overall ITS size. I’m not sure which mission phase is the driver for the ITS propellant tanks and landing engines, but I wouldn’t be surprised if in-space refueling in Mars orbit didn’t cut down both on the overall size of ITS per passenger complement, or if it cut down on the IMLEO of the system. And really, you already have to develop ITS tankers and ISRU on the Mars surface. Just ship a tanker or two along with your original landing group. Use the prop it shipped for refueling the other landers, making sure to leave enough for it to land empty. Even without an actual depot in Mars orbit you can take advantage of that. No new tech, no new elements, but likely a decent savings right from the start. Refuel Early, Refuel Often.
  • Methane Uber Alles: I think Elon oversells his case on how awful Hydrogen is compared to Methane. Sure, for his specific architecture, Methane might make more sense, but I can think of many other architecture where LOX/LH2 could probably be quite competitive for all but maybe Mars Ascent and Landing. Sure, if you insist on having one vehicle do it all, sticking with one propellant makes sense, and sticking with one like Methane probably makes your life easier. But there are so many assumptions baked into that logic chain.
  • Expensive Work In Process Inventory: The major cost driver on the mission is the ITS, because it can only do a Mars trip once per synodic period at best. This is somewhat the nature of the beast for Mars travel–whatever you send to/from Mars is going to take a long time to get there and back, which means you’ll have to amortize its cost over a lot fewer missions. Which is why it would seem like you would want to minimize the cost of the assets that get tied up like that. Having your Swiss Army Knife vehicle be the one that can only fly 12 times in a half century seems like a poor way to optimize for the problem.
  • No Landing Gear on the BFR Stage: I know that my colleagues at Masten also really like the landing-cradle approach, but I’ve never been a fan. Is it doable? Sure. Does it save a lot of cost and time when it works? Sure. But how reliable is it really? I can’t honestly answer this question, but my gut suggests that if your vehicle has a decent chance of surviving landing on an unprepared surface, there are going to be many situations where an abort, a large last second disturbance, or some other error could be survived when a gear-less vehicle is toast. Missing the landing cradle by 10m due to a last-second engine-out scenario probably means loss of vehicle and major pad repairs, where with landing gear it’s a non-event. We could totally build jetliners today without landing gear, using landing trolleys or other things. Or fighter jets landing on sleds on carriers. But we don’t because there’s no way aircraft would be as reliable as they are without having things like landing gear that give them options when something goes off-nominal. Let me put it this way–I don’t think you’re likely to ever see an RLV design that can survive long enough to average 1000 reuses (like SpaceX has baked into their BFR economics) without including landing gear.
  • Crazy Raptor Performance: 4500psi chamber pressure with a LOX-rich preburner sounds like a recipe for fun engine development. This is probably doable, and the Russians eventually tamed RD-180 class engines which have almost as high of chamber pressure, but how reliable will they really be, and how long lived will they really be? I just worry that SpaceX is trying to have its cake and eat it to, by pushing the bleeding edge of performance always, while also trying to push down manufacturing costs and up reusability at the same time. My guess is something is going to give–either the engines will end up being more expensive and finicky, or less reliable than they’ll really want for such a system, or nowhere near as reusable. I just don’t think 4500psi staged combustion seems like a good recipe for a 1000 flight engine. And the failure modes of a 4500psi staged combustion engine when you have 42 of them on your first stage also doesn’t sound likely to be graceful. I could, and genuinely hope I’m wrong. Once again repeating some of the mistakes of the Shuttle by trying to push crazy performance out of their first attempt at a staged-combustion rocket engine.

Ticket Price Economics Thoughts:

  • Per-Vehicle Costs: BFR costs seem to be assuming a per kg cost less than half that of F9 FT. Which seems optimistic to me given the higher performance, more complex engines, and the use of composites for the propellant tanks, and the general scale of the thing. Once again, trying to do a Big Dumb Booster with bleeding-edge performance. But it’s the ITS that I’m really skeptical about. You’re really going to make a spacecraft that has to have all the life support capabilities of ISS, but for 16x the crew, and cram it into a high performance upper stage, a reentry/landing vehicle, and all of that for less than half the cost of a 747-8? Especially given that you’re likely only making a tiny fraction of the number per year. Dragon currently costs probably $30-40M each to produce, and we’re saying that a Dragon designed for 14x the number of people, and 30-50x the duration, with a nearly Saturn V first stage class propulsion system built in is going to only cost 5x as much? Color me extremely skeptical. I think that they’d be lucky to have the production cost of an ITS with all of its subsystems necessary to get 100 people safely to Mars and return reliably down below $1B each anytime in the foreseeable future.
  • BFR Reuse Numbers: I’m also really skeptical they’ll get BFR reliability or engine life high enough to get anywhere near the 1000 reuses they’re claiming. I think they’d be lucky to average 100 flights each once again through the foreseeable future, based on the technology choices they’ve made.

The upshot is that if I’m right on those three items, you’re still talking less than $500M per Mars mission, and a ticket price in the ~$5M per person price range. That’s still three orders of magnitude better than what NASA could realistically do with its architecture. So while I think Elon doesn’t have an architecture that really gets down into the “cost of a median US house” range, he is getting into a range that a lot of people could afford. Having a Mars architecture this affordable would still be absolutely amazing, even if I think it could be done better.

How would I do things differently? Honestly I haven’t put as much thought into it as Elon has, but I have a few high-level thoughts:

  1. Split Things Up More: I’d separate TMI propulsion, the actual transfer habitat, and the Mars to surface and back into three separate elements. If you combine with the next point, the TMI stage can literally just be a normal upper stage like the Falcon 9 upper stage or ACES. The transfer hab would want to aerocapture at Mars, but could do so with a much more modest propulsion, and the Mars landing system can be smaller and higher flight rate. Honestly I think developing three systems that are more optimally split like this will not only cost less to develop than the swiss army knife approach, but will also be lower cost to operate, and open things up more for technology advancements over time.
  2. Go a Bit Smaller: Unless Induced Torpor works out, 100 people in a single vehicle seems really big for the transport stage. Breaking things up into convoys of smaller say 10-20 person vehicles might make more sense. This would mean transfer habitats would be small enough that you could use a TMI stage that is more reasonably sized for use in Cislunar space, so you don’t need a dedicated TMI stage. The transfer habs could be small enough that you have a range of options for aerocapture (inflatable, deployable, in-space assembled, or if it pans out magnetoshell aerocapture). These transfer habs will also have a lot more in common with LEO and cislunar orbital habitats, and possibly early mars surface habitats.
  3. Post TMI or TEI Boostback: I think Dave Masten and I have discussed this in the past, and Robert Zubrin hit on it today in his comments–It probably makes sense to have a separate TMI propulsion system that does the equivalence of a boostback maneuver after the TMI burn is done, to decelerate back into a highly-elliptical Earth orbit, where it can then aerobrake back to LEO. By not sending that along with the transfer hab, you enable it to be reused a lot more, since it’s not tied up for four years now. While not doing transfers to Mars, it can be sending payloads to/from Cislunar space, or to/from GEO. On a similar note, you could send one or two TMI stages along with the transfer habs to serve as TEI stages on the Mars side of things, using a similar post-TEI boostback maneuver and aerobraking to return back to Mars orbit for reuse. The more of your architecture is in the “can get 100+ flights in its lifetime” category vs “synodics mean I can only fly 12x in my lifetime” category, the cheaper things will be overall.
  4. Reusable Horizontal Mars Landers: Having separate landers, possibly smaller than the transit habs makes a lot of sense. The same landers can be used both for hauling people/cargo to/from Mars during arrival season, but also can be used for prepositioning propellant in Mars orbit, and Martian suborbital point-to-point transportation when not being used for Mars arrival landing. Horizontal landing on Mars is trickier than on the Moon, and I’m not totally wedded to the concept, but it seems like a much better way of getting people and heavy cargo onto/off of the surface.
  5. Using LH2 for More of the In-Space Elements: Once you’ve split-up Mars landing/ascent from the TMI/TEI burns, it makes sense to start looking again at LOX/LH2 for those segments. Those are two of the highest delta-V portions of your mission, so the higher performance could help. And LOX/LH2 can be made from Martian, Lunar, NEO, and possibly Phobos/Deimos ISRU sources. I know SpaceX is allergic to LH2, but most of the people I know who’ve worked with it have said “sure it’s a pain, but it’s not as evil as people make it sound”.
  6. Find Ways to Use Transfer Habs for Other Destinations: Say you can only realistically send a reusable Mars transfer hab on every other Mars window. That leaves a decent amount of down-time in-between. If the hab could be used for say taking tourists to/form the Moon or Venus when waiting for the planets to re-align from Mars, you can get much higher utilization out of the transfer hab elements. If you can take the one element in your system that currently can only be amortized over 12 flights (~50 year lifetime), and add in cislunar trips say during the “off-season”, you’re now amortizing it over 100+ flights instead of just 12. If you look at Elon’s architecture, 2/3 of the cost of a Mars ticket is due to the transfer hab’s low number of flights (the same if you make my more pessimistic hardware costs). If you could divide that over 100 flights instead of 12, that would make more of a difference for Mars ticket prices than almost anything else. Could you theoretically do this with the ITS as is? Sure, but without a source of CH4 on the Moon, you’d need to fly a lot more lunar tankers to make that work. Not impossible, but the economics aren’t as good as it would be if ITS could run on LOX/LH2.
  7. Leverage the Moon and NEOs for ISRU More: I still think there are ways that lunar ISRU can eventually beat earth-launched RLV prices for propellants in orbit. Especially if you stage out of a highly-elliptical earth orbit or EML-1 or 2. Investigating if there’s a way to tap into that wouldn’t be a bad idea, and would be a lot easier with the other suggestions I’ve given above.

Anyhow, that’s kind of off-the-cuff, but those are some of how I’d do things differently. As I said above, Elon has a lot of great architecture ideas, but I really don’t think he’s found the “One True Way” to get people to Mars as inexpensively as possible. Worlds better than NASA’s Journey to Mars? Definitely. Technically feasible? Probably. Cheap enough to be interesting? Sure. The best path forward from where we are today? That’s what I’d quibble with.

Posted in Commercial Space, ISRU, Launch Vehicles, Lunar Commerce, Mars, NASA, Propellant Depots, Space Development, Space Exploration, Space Settlement, Space Transportation, SpaceX, ULA, Venus | 58 Comments

I Think I’ve Found a Political Windmill Worth Tilting At

I usually try to keep partisan politics to a tolerable minimum on this blog, and I still intend to. But I had a crazy idea that I wanted to share somewhere other than Twitter.

This year, a significant fraction of the country isn’t happy with either major party candidate. But because of the “first past the post” plurality voting method all states use for selecting their electoral college representatives, it makes it extremely hard for there to be more than two major parties at any given time. You see transitions when one parties goes the way of the Federalists or Whigs, but you never see three major parties stably coexist for very long. There is however no requirement that a state use a plurality voting system to select their electors. For many years, many people have been advocating for alternative voting methodologies such as the Instant Runoff/Preference Voting method (my personal favorite alternative voting method).

For those who don’t want to read the Wikipedia link above, the tl;dr version of Preference Voting is that on the ballot, instead of just making one candidate, you get to rank your order of preference. Ballots are tallied, and if no candidate gets at least 50% of the vote based on everyone’s first choices, the candidate with the least votes gets dropped, and the analysis rerun using the 2nd choices of those voters who picked that candidate. The process is continued until one candidate gets at least 50% of the vote.

The process isn’t perfect, it’s provably impossible to construct a perfect voting system, but if you’re unhappy with the two-party status quo, it’s probably the most practical option out there. It’s currently being used in Australia, New Zealand, Ireland, India, and many municipalities in the US.

The challenge with enacting any alternative election method has always been that how do you get a two party system to enact a law that deliberately limits the power of their two parties?

One fact that helps is that you don’t actually have to do this on the national level to make a difference. A few states have already passed slight variations on the theme of winner-takes-all plurality voting. Nebraska and Maine both have plurality voting by congressional district, with the plurality winner at the state level getting the remaining two electors. But while the Nebraska and Maine approach does make marginal differences around the edges on how many electoral college votes each major party candidate gets, it still stacks the vote against third parties.

What finally got me thinking about an alternative when when I heard about Maine having a ballot initiative this year on whether or not to switch to a “ranked choice” (aka IRV or preference voting) scheme. Unfortunately for some reason they don’t include the presidential election, just governor, their US congressional representatives/senators, and state legislators, but it’s still a step in the right direction.

The nice thing about a ballot initiative is that this provides a potential end-run around the two-party machine in any given state. Admittedly, there are still tons of ways that political parties can oppose such a ballot initiative, but there have been examples of ballot initiatives passing even when strongly opposed by the two major parties.

So, my windmill tilting idea is that I want to figure out if we can get a similar ballot initiative started in Colorado, but this time with the presidential elections included. Here’s several reasons why I think Colorado might be an ideal state for such an initiative:

  1. Colorado has a track record of third party votes already–Ross Perot got nearly 1/4 of the votes in 1992, for instance, and Gary Johnson is currently polling up in the ~15-16% range in the state, and Jill Stein is up around 7% currently, with ~3% undecided.
  2. Colorado is a purple state, which means neither major party has a clear lock on the state. This means that there’s a chance you could get major party voters to vote for this if they thought that their candidate might benefit from more of the 2nd-place votes from 3rd parties.
  3. Colorado requires signatures from 5% of the people who voted for the Secretary of State’s last election in order to become a ballot initiative, but the secretary of state gets elected in non-presidential election years, so the turnout is typically lower–the 98k signatures requirement for a ballot initiative would only be 3.8% of the 2012 voter turnout, for instance.
  4. Colorado has a track record of passing iconoclastic (or at least leading-edge) ballot initiatives like the Taxpayer’s Bill of Rights and the recent initiative that legalized the use of Marijauna.

Here a few thoughts in response to likely questions:

  1. What good will it do if only one state has an IRV voting process for president? First, I think it will likely lead to other states following suit, especially if the experience works out reasonably well. Second, in extremely close presidential elections, even one state going third party could prevent either major party candidate from securing 270 electoral votes, thus throwing the election to the House of Representatives. In the house, each state delegation only gets one vote, and the vote can only be for the three candidates with the highest electoral vote counts. In the case of a close presidential election, I think this would potentially give a benefit to compromise candidates who can appeal to members of both parties.
  2. Wouldn’t Preference Voting be more confusing for voters? According to the Wikipedia article, “In American elections with IRV, more than 99% of voters typically cast a valid ballot1.” This seems like a solvable problem.
  3. Isn’t it too late to get this on the ballot for 2016? I think so. But in some ways it might be better to start pushing for this in the next election. If this year’s presidential election is close, especially if the margin of victory is less than the third party vote, voters for whichever major party loses in Colorado might be swayed to support this initiative if one can make the plausible argument that their candidate would’ve benefited from being the 2nd choice of third party voters. Frankly if you’re a Democrat that thinks Ralph Nader cost Al Gore the election in 2000, isn’t that functionally the same thing as saying you think Al Gore would’ve benefited from a preference voting system? Ralph Nader only cost Al Gore the election if Al Gore was really the second choice of enough Nader voters to have tipped the Florida election to Gore if Nader hadn’t been on the ballot.

It’s still a long-shot, but I think this is a really good idea, especially with the bad taste many people will have in their mouths from this year’s presidential election. I think I’ve found a political windmill well worth tilting at.

Posted in Politics | 25 Comments

Energy needed to get to orbit using various fuels from various planets.

EDIT: I made a big mistake on how I calculate bulk density. I’ll fix it. EDIT AGAIN: I fixed it. I think.

I will pick stoichiometric mixes, oxygen as oxidizer and fuels of hydrogen, methane, and carbon monoxide. The three most obvious ISRU fuels (to me anyway). Picking stoic, I will also assumption that mass fraction (sans payload) is inversely proportional to bulk density. And at water density, I’ll say a mass fraction of 30 is doable, i.e. if wet mass is 30 ton (not counting payload), dry mass (not counting payload) will be 1 ton.

oxygen density at 90K and 1MPa: 1144kg/m^3
hydrogen density at 20K and 1MPa: 72.41kg/m^3
methane density at 111K and 1MPa: 424.2kg/m^3
carbon monoxide density at 81K and 1MPa: 798.2kg/m^3

Oxygen atomic mass is 16
carbon is 12
hydrogen is 1
stoichiometric ratios by mass:

We’ll use this equation for bulk density (thanks those who commented!).
bulk density = 1/(MR/fuel_density+ (1-MR)/oxidizer_density)

H2 + (1/2)*O2 = H2O So, 1:8 fuel:oxidizer, bulk density: 1/((1/9)/72.41+(8/9)/1144)kg/m^3 = 432.6kg/m^3
CH4 + 2*O2 = 2*H2O + CO2 So, 1:4 fuel:oxidizer, bulk density: 1/((1/5)/424.2+(4/5)/1144)kg/m^3 = 854.1kg/m^3
CO + (1/2)*O2 = CO2 So, 7:4 fuel:oxidizer, bulk density: 1/((7/11)/798.2+(4/11)/1144)kg/m^3 = 896.8kg/m^3

Turns out, stoichiometric is probably a very bad assumption for bulk density as hydrogen looks better than everything else. (But this is an interesting and useful result anyway.) EDIT:Just kidding, I was super wrong about bulk density the first time I did this. I should’ve known better! The TRUE result means CO/O2 has a better bulk density than the other options, which is more like what I expected.

Second assumption I’ll make is that rocket engines are exactly 50% efficient at converting chemical energy to jet energy. This is a conservative assumption, I think.

And the specific energy of the fuels (not counting oxygen mass) is:
hydrogen: 142MJ/kg, with oxygen: 15.8MJ/kg
methane: 55.5MJ/kg, with oxygen: 11.1MJ/kg
carbon monoxide: 10.1MJ/kg, with oxygen:6.43MJ/kg

specific kinetic energy is: .5*mass*velocity^2/mass = .5*velocity^2
So if the propellant mix specific energy is F, but we’re only 50% efficient so the energy effectively put in the velocity of the exhaust is .5*F. Setting that equal to specific kinetic energy:
solving for velocity:
velocity = sqrt(F), so the effective exhaust velocities of the above fuels are:
hydrogen: sqrt(15.8MJ/kg) = 3975m/s
methane: sqrt(11.1MJ/kg) = 3330m/s
carbon monoxide: sqrt(6.43MJ/kg) = 2535m/s

So the burnout velocity of stages would be:
hydrogen: 3975m/s*ln(30*.4326) = 10.19km/s
methane: 3330m/s*ln(30*.8541) = 10.81km/s
carbon monoxide: 2535m/s*ln(30*.8968) = 8.34km/s

If instead we fix mission delta-v at 9km/s, 8km/s (we’ll assume we get a bonus from getting high altitude balloon-launch automatically at Venus…), and 4km/s for Earth, Venus, and Mars, respectively, the mass of payload as a multiple of the rocket dry mass is:

hydrogen: (30*.4326-e^(9/3.975))/(e^(9/3.975)-1) = 0.3890
methane: (30*.8541-e^(9/3.33))/(e^(9/3.33)-1) = 0.7715
carbon monoxide: (30*.8968-e^(9/2.535))/(e^(9/2.535)-1) = -0.2333

hydrogen: (30*.4326-e^(8/3.975))/(e^(8/3.975)-1) = 0.8476
methane: (30*.8541-e^(8/3.33))/(e^(8/3.33)-1) = 1.4533
carbon monoxide: (30*.8968-e^(8/2.535))/(e^(8/2.535)-1) = 0.1538

hydrogen: (30*.4326-e^(4/3.975))/(e^(4/3.975)-1) = 5.902
methane: (30*.8541-e^(4/3.33))/(e^(4/3.33)-1) = 9.604
carbon monoxide: (30*.8968-e^(4/2.535))/(e^(4/2.535)-1) = 5.741

But we want this in terms of energy, so we’ll start with expressing as a proportion of propellant and then as energy:

hydrogen: 0.3890/(30*.4326-1)=0.03248 (kgpayload/kgpropellant)
methane: 0.7715/(30*.8541-1)=0.03133
carbon monoxide: (negative)

hydrogen: 0.8476/(30*.4326-1)=0.07077 (kgpayload/kgpropellant)
methane: 1.4533/(30*.8541-1) =0.05902
carbon monoxide: 0.1538/(30*.8968-1) =0.00594

hydrogen: 5.902/(30*.4326-1)= 0.4927 (kgpayload/kgpropellant)
methane: 9.604/(30*.8541-1) = 0.3900
carbon monoxide: 5.741/(30*.8968-1) = 0.2216

Payload per unit energy (kg/MJ):
hydrogen: .03248kg/(15.8MJ) = .002056kg/MJ
methane: .03133kg/(11.1MJ) = .002823kg/MJ
1carbon monoxide: (negative)

hydrogen: .07077kg/(15.8MJ) = .004479kg/MJ
methane: .05902kg/(11.1MJ) = .005318kg/MJ
carbon monoxide: .00594kg/(6.43MJ) = .000924kg/MJ

hydrogen: .4927kg/(15.8MJ) = .03118kg/MJ
methane: .3900kg/(11.1MJ) = .03514kg/MJ
carbon monoxide: .2216kg/(6.43MJ) = .03447kg/MJ

Also, I’ll add the more convenient form of the above:

Energy per kilogram payload Efficiency
H2/O2 486.492201 MJ/kg 0.08324902212
CH4/O2 354.2839962 MJ/kg 0.1143150705
CO/O2 -713.873967 MJ/kg -0.05673270335

H2/O2 223.2713187 MJ/kg 0.1433233797
CH4/O2 188.0569743 MJ/kg 0.1701611978
CO/O2 1082.792097 MJ/kg 0.02955322642

H2/O2 32.06682927 MJ/kg 0.2494789844
CH4/O2 28.45933589 MJ/kg 0.2811028349
CO/O2 29.01123497 MJ/kg 0.2757552379

Methane appears to be optimal for the SSTO case (though I think hydrogen pulls strongly ahead as the upper stage in the two stage case), as you would expect because of the higher stage burnout velocity. Or methane would be most optimal on other planets (where you have to get propellants through electrolysis), if its production were more efficient. Because, although hydrogen and carbon monoxide can be produced directly from electrolysis of water and carbon monoxide (respectively), methane requires a Sabatier reaction step, which loses some energy in the form of heat. Additionally, CO2 is ubiquitous on both Mars and Venus.

This is obviously simplistic, but an interesting result. I should’ve just done this in a spreadsheet. I did this in a spreadsheet now.

It kind of gives impetus to Jon’s oxygen-rich hydrolox engine idea. When your run ox-rich, hydrolox actually has very high bulk density. (This was sooo wrong… thanks, commentators, again.) Really, you’d want to optimize your Isp as you ascend, particularly on Mars. It might even make sense to blend in some CO2 at first as just reaction mass.

The exhaust velocities here are pretty pessimistic (although stoic is not a very good assumption, either).

We looked at efficiency by dividing the specific energy by (.5*(9,8,4 km/s)^2).

The efficiency of rockets isn’t too bad. Partly that’s because we used stoic. Also, this is mission delta-v which includes some losses (i.e. aero and gravity). However, we can do much better by using multiple stages and especially interestingly by playing with mixture ratios.

I think I’ll next do an analysis looking at dry mass required with more realistic propellant mixes.

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Reverse Rocket

This is a post about an idea by Doug Plata. His idea is to put multiple propellant tanks on top with just enough structure to keep them intact and drop them in pairs as they drain. Under the tanks is the payload. Under the payload is a plug nozzle/heatshield that multiple engines expand against for altitude compensation. The configuration is chosen to be fault tolerant of both engines and tanks. This allows the use of somewhat questionable engines and tanks. The concept is specifically for the purpose of launching very large payloads on vehicles with relatively low development costs.

From the top down, this concept starts with a composite aerodynamic fairing that is also a fuel tank for kerosene. Next is a cluster of 19 tanks each of which holds either fuel or oxidizer with no common bulkheads. Next comes the payload volume which is the full diameter of the 19 tanks and whatever length required for the particular mission, with cylindrical sections added or removed as required. Under the payload volume is a full diameter plug nozzle that is also a heatshield for reentry. Against the sides of the plug nozzle are multiple engines of relatively low expansion ratio with the plug nozzle making up the difference at all altitudes.


The cartoon is a rough representation of Dougs’ concept. The payload can be a habitat cylinder 15 meters in diameter and 30-45 meters long. By launching it dry, all of the permanent fittings can be installed and tested on the ground as well as some of the transient components that are used early on.

The habitat is conceived as useful for an all up station in one go without the fitting problems of an expandable structure that is volume constrained at launch. It is also possible to design it in such a way that lunar mass could be added for radiation shielding in Lunar orbit or one of the L points. The rigid structure is also suitable for the Lunar surface with the capability of handling a thick regolith covering

The aerodynamic fairing that is also a fuel tank is handles aerodynamic loads only with both the fuel and pressurant gas providing support through the atmospheric portion of the flight. It is expected that mass of the shroud/tank will be on the order of 2% of the mass of fuel it holds. The shroud tank is sized to empty as the vehicle reaches low dynamic pressure at altitude when it is jettisoned.

The 19 tanks under the shroud/tank are protected from  head on pressure while in the atmosphere. As the shroud tank is jettisoned, the empty oxygen tanks in the 1 ring are sent off as well leaving only full tanks to carry. As each pair of either oxygen or kerosene tanks are drained on opposite side of the vehicle, the empties are kicked off from the 1 ring, then the 2 ring. The pressurant gasses in each tank are used as a cold gas thruster to ensure clean separation. There are as many as 6 tank staging events as the vehicle climbs out. Each tank being 3 meters diameter by 50 or more meters long, available propellant volumes are at roughly 350 cubic meters per tank. Tank mass can be on the order of 1% of propellant mass. Along with the shroud/tank, propellant mass can be on the order of 7,000 tons.

At the plug nozzle/heat shield, there are as many engines as required by a given mission. Since the concept is for launching massive one off missions, engine mounting must be modular similar to the tank concepts. Shrapnel shields and other safeguards must be designed in as the concept is for very low flight number vehicles with inherent infant mortality. Extra engines are a requirement for a couple of reasons. One is that it allows a more efficient flight profile than the normal thrust limited take offs of most launch vehicles. The other, more important reason is that available engines will be used with variable reliability and  availability. Careful attention to this detail should make it possible to use the remaining AJ-26 inventory of orbital-ATK as well as used Merlins and anything else the contractor can get his hands on. Unreliable engines can be compensated by having fail safe ways of shutting them down and jettisoning them. This approach allows buying engines from motivated sellers.

An additional advantage of Dougs’ concept is that it allows the multiple engines to use a variety of propellants. A mixture of kerosene, methane and hydrogen engines is quite possible in this configuration.

As the vehicle sheds propellant and tank mass, acceleration will rise. As it reaches the maximum desired, pairs of engines will be dropped in a manner similar to the way the tanks are treated. Each engine can be fitted with a decelerator and parachute as long as the velocity is low enough that there is a reasonable expectation of recovery. At higher velocities, expended engines will be lost as they are dropped. The ones that make it to orbit can be packaged into the heat shield for return to the ground.

The plug nozzle/heat shield has a multiple use as a heat shield in addition to its’ nozzle duties. In case of abort, engines and tanks are jettisoned and the heat shield  is used to protect the payload for a return to sea level. The idea is that the nozzle and vehicle shell may be lost, but the interior equipment could be saved for use on a replacement mission. For returning the payload from orbit, or atmospheric entry to another planet, the heat shield works in the normal manner. On a nominal mission where the payload is not returning to Earth, the heat shield is used to return the remaining engines and any other valuable gear that needs to return to the ground.

Figuring the payload to orbit is interesting. It turns out that with so many small staging events, the dropped tanks and engines can be treated as propellant for calculation purposes. With ~7,000 tons of Kero/LOX propellant, it is possible to place a 350 ton space station in orbit with well over 6,000 cubic meters of living and work space.  This is moreover, work space that doesn’t have to be cramped into tiny cubicals and corridors.

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Getting My Numbers

This is an explanation of how I get BOTE numbers for such things as the comparison between LH2 and CH4 propellants as in Jons’ last post.

The focus Jon had was how much H2 do you need to carry to Mars or Venus to get a return stage if you do a straight LH2/LO2 as opposed to using in situ resources to create CH4 with the hydrogen you carried from Earth. If it was just as effective to use the hydrogen directly as using the intermediate step of converting it to methane with local carbon, then why bother with the conversion and the equipment required to carry it out. Also, if using a hydrogen stage for Earth departure, commonality of equipment is a plus for using a hydrogen stage for Mars or Venus departure. In effect, it is possible that the use of local carbon to convert the on board carbon to methane might not be a worthwhile step.

I is not a rokit sceintest so I tend to look for simplifications that I can do with a scratch pad and TI 30 calculator. A real rocket engineer calculating real missions will go far more in depth than I am capable of, but he tends toward getting paid for his efforts. So this method is worth almost what you are paying for it.

I picked Mars as the launch site for this BOTE because it is easy. I figured 6,000 m/s total V for the rocket because it seemed like a good start for a vehicle that has to reach Mars orbit and do other things once it gets there. Other things range from rendezvous with Earth departure vehicles to a surface return for more flights. If there were a good reason to figure a different V, you can do it during lunch and still have time to eat.

6,000 m/s stage with hydrogen figured as 4,500 m/s exhaust velocity and Methane as 3,700 m/s. Rocket equation gives mass ratios.                                                                                 propellant type                                          hydrogen                                      methane                     mass ratio                                                     3.79                                                 5.06

Then I translate mass ratio to percentage of propellant at lift off.                                                percent propellant                                                74%                                                 80%                propellant density                                               0.31                                                  0.94                 tank volume per ton                                        3.26 meters                                    1.05 meters     tank mass per ton at 20 kg/cu m                   65.2 kg                                               21  kg             tank mass as percent of GLOW                         4.8%                                                1.68%              engine T/W est                                                   80                                                       110                engine mass at 6 m/s at GLOW                        0.75%                                                0.5%             percent of propellant, tank and engine           79.55%                                               82.18%          percent payload to GLOW                                20.45%                                              17.82%        Glow per ton of payload                                      4.89 tons                                          5.61 tons      propellant mass per ton of payload                    3.6 tons                                           4.5 tons       hydrogen percent of prop load                              14.28%                                            6.25%          hydrogen per ton of payload                                 0.514 tons                                      0.28 tons

This is all just a fast way of getting a BOTE for a concept. Anyone could change a variable and have an answer for a different scenario in a few minutes. To me, the question that Jon posed is an interesting one. Is it worth doing all the conversions in favor of somewhat more hydrogen tankage?    I had assumed it was. Now I don’t know. It will take a detailed trade study for a specific mission set up to see which is better, or neither. Comments on Jons’ post brought up CO for a first stage. Another mentioned perchclorate in the Martian regolith at ~1% concentrations.

I think it is fair to say that there are far more possibilities than we normally consider, and that good answers are not always the most obvious ones.




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Random Thoughts: Which is a Better ISRU Propellant on Venus/Mars–LOX/LH2 or LOX/CH4?

I’m not sure if someone has already run the analysis, but I’m kind of curious about which ISRU-derivable propellant combination is better for locations like Venus or Mars where there is plenty of CO2 available in the atmosphere, but limited water.

Assume for a second that water isn’t available in useful quantities. I’m not sure yet if the concentration in the Venusian atmosphere is high enough to be useful, and it’s not yet clear that there’s easily accessible water at most places on Mars–there might be, but it’s far from clear1. Assume for now that you have to bring your hydrogen with you, from Earth.

A few quick observations:

  1. One immediately obvious point is that if you have to BYOH2 you’ll probably want to bring the hydrogen as LH2, not water. While everyone complains about how hard it is to store LH2 for long durations in space, water is still ~89% Oxygen, which is a material you can get almost anywhere, especially if you have CO2 available, so for every kg of hydrogen you bring tied up in water, you’re lugging around an unnecessary ~9kg of oxygen. You can definitely make a dewar with active cryogenic cooling that masses far less than 9x the mass of LH2 you want to bring with you–it may be “harder” to do it that way, but is far, far more efficient.
  2. A typical O/F ratio for LOX/CH4 is probably around 2.8-2.9:13, which means that about ~6.5% of your propellant mass is hydrogen for LOX/CH4. For LOX/LH2, you’re probably looking at an O/F ratio of around 5-6 typically, which would yield ~14-17% hydrogen. So for every kg of hydrogen you bring along, you could get4 ~15.4kg of LOX/CH4, or you could get 6-7kg of LOX/LH2.
  3. If you’re limited by hydrogen you can bring, rather than dry mass, or volume, or other things, it’s not yet clear which of those will result in more payload in orbit, since the two have significantly different bulk densities and Isp values. That’s the analysis that would be fun to run. My guess is a lot will depend on the required delta-V5, whether you’re looking at 1, 2, or 3 stages, if you assume on-orbit refueling before the earth-return, etc.
  4. One way to cheat a little with LOX/LH2 would be to use a LOX-rich Thrust Augmented Nozzle (TAN). Basically, you have a core running at the more traditional 5.5-6:1 O/F ratio, while initially running the afterburning portion of the engine at a much higher mixture-ratio, possibly even higher than stoichiometric! As the rocket accelerates, you could throttle down this element and then shut it off. This is probably more useful for Venus ascent than Mars, but would allow you to get not only a much higher engine T/W ratio than you could realistically get normally with LOX/LH2 engines, but also give you more propellant per kg of brought hydrogen, because you’re shifting your mission-averaged mixture ratio to a very, very lean range.

I honestly don’t know the answer, and don’t have time yet to run the numbers, but I’m genuinely curious. If you have a fixed supply of hydrogen, which ISRU propellant method (using a Sabatier reactor to convert H2 and CO2 to LOX/CH4, or using a solid electrolysis cell to crack O2 out of the CO2 to make LOX/LH2) actually yields the most mass delivered to orbit or to an Earth return trajectory from Mars or Venus? Has anyone already done this analysis? If not, I may try to find some time at some point to run the numbers.

[Update 9:58pm on 9/5/2016: in case you’re curious what brought this on, I was thinking about Venusian Rocket Floaties again, and was wondering whether a Venusian launcher first stage would want to be LOX/CH4 or LOX/LH2.]

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Semi-Staged Combustion

It is interesting comparing the two best known first stages in the US that use kerosene and LOX. The Atlas 5 and the Falcon 9 use a similar fuel in their first stages and then diverge in the technical aspects. The Atlas 5 with the RD 180 engine has about 10% higher Isp at sea level while the Falcon 9 Merlin has nearly twice the thrust/weight ratio. The over all Falcon 9 first stage seems to have a much lower dry mass ratio which makes up the difference in engine performance and then some.

There are going to be new vehicles designed by the various companies eventually that would like to benefit from the competitive advantages of both vehicles. A high thrust/weight ratio engine with high Isp that also has low dry mass is a desirable target. The more these features can be designed in, the more mass is available for payload, reusability, or both.

One of the engine cycles that is discussed from time to time is the dual chamber concept. It is more or less a gas generator cycle with an exhaust pressure high enough to inject into a lower pressure thrust chamber to burn with fuel or oxidizer to get useful thrust. I suggest it might be possible to get very near RD 180 Isp with very near Merlin thrust/weight with a variation of the concept. A low stage dry mass being part of the goal, I add in a few features that may be unique.

Semi-Staged CombustionIn the cartoon I have two high pressure chambers on the outside with a lower pressure chamber in the middle with an altitude compensating nozzle.

The black boxes in the tanks are the electric inducer pumps from the previous post.  They are to keep the propellants at high enough pressure to the main pumps to suppress cavitation as well as keeping required tank pressurization to a minimum.

The small blue tanks in the inter tank area are for the liquid hydrogen that serves multiple purposes. First the hydrogen feed hits a heat exchanger in the LOX  tank to keep it cold enough to stay liquid and suppress cavitation even as tank pressure drops. Then it hits a heat exchanger in the RP tank for the same purpose. Then it is used to cool the turbine blades the same way that jet engines use air cooling. Finally it burns with the excess LOX from the gas generator to produce thrust.

With the pumps providing pressures to the main engine similar to that of the RD 180, the Isp of them should be similar. About 10% of the propellant goes to the gas generator driving the pumps with a residual pressure of 300 psi after the turbine. If the 300 psi engine was a normal kerosene engine, one would expect an Isp in the 250s from that portion of the thrust system. With the lean (LOX rich) gas generator driving a hydrogen cooled turbine at much higher than normal turbine inlet temperatures, the warm hydrogen mixes with the hot oxygen as it is used for film cooling of the blades and burns in the secondary chamber above the throat. The hydrogen/kerosene/LOX engine at 300 psi could approach the ISP of the main engines due to the higher performance of hydrogen. Hydrogen usage will be a fraction of a percent of the total propellant load.

The compensating nozzle of the low pressure engine in the center would allow reasonable Isp of that portion at sea level, especially with the hydrogen component. The higher expansion ratio made possible would allow much higher Isp at altitude, which, with the hydrogen component, could give vacuum Isp higher than the RD 180. I think the potential result is low hardware mass combined with high first stage performance.

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Electric Inducer Pump

It takes pressure in the tank to suppress cavitation in the pumps for rocket engines. It is customary to use helium for most pressurization due to its’ low molecular weight. Unfortunately, it can take a lot of helium in some cases. Some propellants can self pressurize under the right conditions, though here is where the molecular weigh becomes important. O2 with a molecular weight of 32 is eight times the mass of helium at 4.

Heating up the pressurant gas helps considerably, though helium can be heated up as well. Sub-cooling the propellant helps suppress cavitation and allows a lower pressure in the tank to be effectively pumped. I am going to suggest an inducer pump in the tank instead.

If the required pressure in the tank can be reduced from 30 psi or more to 5 or so as the vehicle reaches altitude, the pressurant gas quantity can be reduced by a factor of 6.  An electric inducer pump in the tank might make this possible. A pump that is bypassed early in the flight is gradually brought online with increasing power as the tank level drops and with it the head pressure.

header pumpThe waste heat from the pump can be used on the pressurant gas to reduce the required mass. The pump power can be gradually increased to keep a constant 100 psi  or whatever the spec requires to the turbo pumps.

The objections I have had in the past to electric pumps have mostly to do with the mass penalties of the electric motors, and to a much greater extent the battery mass to reach engine pressure. A relatively low pressure pump used as an inducer gets around some of this. If pressurant gas is reduced along with the elimination of their tanks, that should compensate for the all of the motor weight and some of the battery weight. If the batteries are those of the satellite payload, then there might even be a mass savings. Many of the satellite payloads have a considerable amount of their mass in batteries which might as well help haul the freight during launch when they are probably bored anyway.

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Notchbell Nozzle

Several years back I suggested a type of compensating nozzle that should be inexpensive to build and test. Unfortunately the ones I made for demonstration with compressed air were hit and miss as I didn’t have the theory quite right. Hit and miss is not good enough for serious companies, so I mostly dropped the idea for a while. I thought a few of my acquaintances in the business might do something with the idea for a while. Now I think the idea has  been mostly forgotten as unworkable.

A few years back I did finally find the missing part of the concept and did nothing about it as I thought at the time that others had picked it up and moved on. Since I don’t think that has happened, I am going to repost the concept.


On the left is the engine with the notch showing on the right side. The notch allows the atmosphere to enter the bell to compensate for over expansion at lower altitudes. At higher altitudes and in vacuum the exhaust gradually uses the whole bell with some losses through the notch. This will allow a nozzle to be optimum at sea level when most are over expanded. It will also be nearly as good as a full diameter high expansion nozzle in regimes with the exhaust under expanded.

The missing ingredient in the prior concept was appreciation for the momentum of the exhaust at the notch site. The momentum, especially with the rounded notches that I was advocating before, would prevent the atmosphere from entering the notch in a controlled manner. The addition of a sharp edge at the notch to assure a clean break and a slight reverse on the notch edge to direct the exhaust inwards controls the momentum of the exhaust in a manner that allows the atmosphere to interact and provide pc/pa compensation at a range of back pressures.

A compensating nozzle allows lower pressure engines to operate more efficiently in a launch vehicle. They should allow a payload increase of 1-5% depending on the vehicle and the assumptions going in. For a VTVL that wants to operate at very low pressures in the landing phase, a compensating nozzle would be a very important upgrade, though the successes of Blue and SpaceX take some of the edge off that argument.

This is a public domain concept as I described it here years ago. So anyone that wants to see what I am talking about can build a quick and dirty nozzle to use with shop air. The ones have done were an air chuck and fiberglass. About $10.00 in materials. I know it works at 135 psi. Then you can try a higher pressure gas if it might be useful to you or someone you know.

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