Airbreathing hypersonic travel is less energy efficient over long distances than rocket travel

There’s a certain misunderstanding common in aerospace that rockets are horribly inefficient and that long term we need air breathing ramjets or scramjets to efficiently launch things, with the idea that we can thus avoid accelerating oxygen to flight speed, which is considered wasted energy. “Airbreathing hypersonics are five times as efficient as rockets” they say. This, however, is not so.

The misunderstanding comes in part by considering oxygen as just as costly as fuel. Oxygen is not. It can be condensed out of the atmosphere with little energy and is available by the truckload at $100/ton or less. A dedicated production plant can produce it for as low as $10/ton. That compares to $1200 to $3500 per ton for industrial liquid hydrogen which is often the fuel being compared to.

A stoichiometric rocket burns 8 times as much oxygen as it does hydrogen. So if an airbreather consumes a factor of 5 times less propellant than a rocket, that means it consumes nearly twice the hydrogen!

Hydrogen requires the vast bulk of the energy to produce compared to oxygen, a couple orders of magnitude more energy. So for our purposes we can ignore the energy needed to produce liquid oxygen.

Let’s look at LAPCAT II, and airbreathing hypersonic airline concept capable of traveling to the antipodes of the world at Mach 8.

As a percentage of its gross takeoff weight, 45% is hydrogen fuel and 15% is payload:

That means each kg of payload requires 3 kg of liquid hydrogen, which has an energy density of 142MJ/kg, giving an energy cost of 426MJ per kilogram of payload.

Hydrogen with variable mixture from oxygen rich to near stoichiometric would be the best fuel to compare with and the most efficient for rockets, but I will use SpaceX’s ITS from 2016 as a comparison point even though it’s less energy efficient.

ITS has a payload to LEO of 300 tons (more for the tanker variant), and uses a total of 6700 tons of propellant for the first stage and 1950 tons for the second stage ship (both including landing propellant). Given a O:F weight mixture ratio of 3.9, and a specific energy of 55.5MJ/kg for methane, the cost per kg of payload to orbit is just 330MJ, actually less than the hypersonic airliner in spite of using less efficient methane.

You might as well use rockets for long distance transport at high Mach numbers.

Posted in Uncategorized | 37 Comments


Hey guys, just FYI at Chris’s request (and with some help from Mike Mealling), I updated the website to add SSL encryption and use https instead of http. Apparently, Chrome is about to start giving people warnings if they visit sites that aren’t secured properly.

Also, it’s been a while since I’ve blogged–I’ve been in proposal hell for a while and am only finally coming out of that mode, but I wanted to mention that I’m planning on doing some posts soon reviving the previous thread on Venus ISRU and Settlement issues. More later.


Posted in Administrivia | 1 Comment

Plan D for space settlement

Plan D
There are three companies I take seriously for making true spacefaring (ie including Mars because I’m a Mars Firster) truly accessible: SpaceX, Blue Origin, And Masten Space Systems. I would have taken XCOR seriously, but unfortunately they went bankrupt.
The other three:
1. SpaceX. By far the top of my list. Fast execution, well-capitalized when they need to be, sustainable, good business plan to scale up to $100 billion level, and great architecture. Actually hard to improve on this one. But SpaceX got where it is on the shoulders of Elon Musk and by taking a lot of risks. The flip side of that is one of their bets could go far south, or something happens to Elon. Don’t want to rely on one, particularly risk-taking, company.
2. Blue Origin. Somewhat a mystery, but ridiculously well capitalized. Sustained by brute force money injections, not (much) actual business yet. Similar near-term architecture to SpaceX, but slower & not quite as aggressively low cost. Not easily extendable to other planetary bodies without separate development (which apparently they’re doing with Blue Moon). Moon and free space focused, so I wonder if they’ll even get around to Mars before I’m elderly.
3. Masten Space Systems. Very small, poorly capitalized, but actually pioneered a lot of the reusable tech SpaceX uses. More experience with reusable rocket vehicles than anyone. Was looking like a real possibility for highly reusable launch before Boeing sadly won the XS-1 DARPA bid. Now has pulled back and seems focused on small commercial lunar landers. But unlike XCOR, they’re still in the game.

Plan D? Still thinking about it. But I think a rapid return to launch pad thing like BFR and Masten is a good plan, although ambitious. Fast integration of upper stage is key as well. I like Jon’s idea of an oxygen-rich hydrolox architecture.

Posted in Uncategorized | 11 Comments

Your Sweat Given Rights (Off Topic)

I would like to introduce a possible new term to help counter the seemingly increased use of “God Given Rights” by lawyers, politicians, and various activists that wish latch onto or hand out other peoples’ resources and freedoms. This particular rant was inspired by an ad on the radio today by a lawyer. “You have a God Given Right to a good job, a living wage, a safe living environment, good food, and so on. Followed by a list of possible reasons to call him so he could force them to deliver yours. Included were brags about how much he had won for deserving clients.

I would like to propose the sound bite “Sweat Given Rights” to indicate to people that all these desirable outcomes have to be paid for by the sweat of  someone, often someone else. That good job was created by someone that earned it, often with long hours and personal financial risk. Same with safety, nutrition, medical care, and education among other desirable  services most of us want. Someone has to sweat to provide whatever desirable thing we want and I think it is past time for the word war to start a reasoned counter attack. Reasoned in today’s world mostly isn’t going to be scholarly tomes invoking the Constitution, or interpretations of biblical verse that are obscure to any not already knowledgeable.

I would prefer TANSTAAFL  except that it doesn’t sound bite well enough to get through to many that aren’t going to research issues. Aggressively looking for simple soundbites to counter bad memes might well be one of the important tools to stemming some of the abuses by well meaning people that are following  bad leaders and getting bad advice.

This phrase doesn’t imply throwing people out on the streets to die. It simply reminds some that might listen that TANSTAAFL.


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Megacharger costs… (Tesla Semi Part Two)

Elon Musk announced the Tesla Semi months ago, now. Besides the low cost, one of the things people are most incredulous about are the Megacharger costs. Tesla announced just 7 cents per kWh, flat price, to charge at a Megacharger. And that’d be done with solar power, potentially even unhooked from the grid. How is this feasible?

First we must look at existing Tesla Superchargers. Superchargers are capable of up to 145kWh charge rates (internally). Some versions were made by simply ganging up multiple home charger units together to get the required power (like 12 individual 12kW units). The high power was produced by clustering mass-produced smaller units that also are provided with each car. Just a single connector goes to each car, however.

Superchargers use a very large amount of power. A bunch of supercharger stalls being used at once at a Supercharger location can draw Megawatts. Simply installing a megawatt connection to the electric grid is expensive. So Tesla has started installing Powerpacks (the larger versions of the Powerwall designed for utility and commercial installations… around 210kWh apiece… themselves composed of 16 individual battery packs similar to those used for the Model S/X/3 and each with a DC-DC converter, with a DC-AC inverter of between 50 and 500kW of output, depending on configuration). This allows Tesla to add additional supercharging stalls to existing supercharger locations without upgrading the utility connection, and for new locations allows them to avoid utility peak charges which could actually end up being larger than the actual energy usage charges. As a side benefit, it also means that Superchargers have backup power in case of power outages:

…and in principle, Tesla could also optimize when the Powerpacks are charged to minimize time-of-day charges. That gives Tesla access to sub-7-cents-per-kWh electricity prices already. Industrial electricity prices are around 5 to 8 cents per kWh on average in the US (exception is Northeast, with about 9-12 cents per kWh), with off-peak electricity being about 2 or 4 cents per kWh less.

So Tesla probably ALREADY pays less than 7 cents per kWh for electricity on average. But they also have a significant amount of capital cost in the form of the chargers themselves and the batteries. The Batteries go for about $400/kWh retail, but Tesla’s internal price may be more like $150-250/kWh, especially without the inverter. That’s about 3 cents per kWh if they last for 20-25 years (which isn’t actually too unreasonable, given careful charging and discharging). 4 cents is more reasonable. But long-term, they hope to get cells below $100/kWh, and packs at, say, $120/kWh. (Raw material costs are about $35-45/kWh.) So <2 cents per kWh for the packs themselves is feasible, especially if they can get them to last a while. And ultimately, these packs can be assembled in an automated fashion, like their Model 3 packs. In fact, they could actually use the same battery line. (The biggest argument against automation is, like reuse, that it's not worth it at the volumes Tesla is considering, but if the same line is producing fairly standardized packs for multiple uses, that can dramatically improve the automation business case.)

But if you already are using battery packs for peak power reduction and maybe even time of day shifting, then the idea must occur to you: why not get rid of the utility entirely?

Solar cells are currently as low as 16 cents per Watt on the spot market (average 17.5 cents), without federal subsidies: That means 16 cents of cells produces 16 cents of electricity (at 7 cents per kWh) in a SINGLE year in a place like the American Southwest that has a capacity factor of about 26% or better, paying back the cost of the cells. Modules are more, obviously, but still cheap at 27 cents per Watt. If Tesla can automate installation, they may be able to install them and string them together for less than 40 or 50 cents per Watt. That doesn’t pay for a connection to the grid or the inverter. Because Tesla doesn’t need those. In fact, the batteries already contain a DC-DC converter. Careful selection of voltages could allow a nearly direct connection of the solar panels to the batteries, perhaps with a small and cheap “power optimizer” (i.e. DC-DC converter) to improve solar array efficiency. These things only cost a few cents per Watt at utility scale, so let’s call it an even 50 cents per Watt. But Tesla can avoid the grid connection at both the solar array side AND the Supercharger side. And can avoid the cost of the inverters and the inefficiencies/losses from converting to and from AC. That previous 210kWh Powerpack thus has more like 225kWh. And over 25 years, therefore, a solar array that costs just 50 cents per Watt to install means electricity at less than 1 cent per kWh (0.9 cents) in a place with 26 percent capacity factor. However, there are sometimes cloudy days, where solar arrays will be less effective. To counter-act that, we make the solar array about twice the size. Cost per kWh doesn’t quite double, however, as not all the balance-of-system costs double. So let’s say 1.5 cents per kWh. Batteries also need to be about double, so cost of the battery is about 4 cents per kWh total, maybe less. But total cost of electricity is thus just 5.5 cents per kWh, leaving room financing costs. Doable if financing can be kept at low costs (and the solar arrays can actually last a LOT longer, like 50-100 years… and by doubling up the batteries as we did, they can also last a lot longer). And remember, solar costs will continue to decrease, long-term (tariffs notwithstanding). 3 cents per kWh raw solar+battery costs and 5.5 cents per kWh assuming roughly doubly up number of both li-ion and photovoltaic cells.

So that’s how Tesla can offer 7 cents per kWh for the Tesla semi while disconnecting from the grid and using solar power.

Posted in Uncategorized | 7 Comments

Repost of an Idea

Some years ago I did a post on using Lunar fuel to raise a sub-orbital vehicle to Earth orbit. One of the comments by sjv linked to a similar concept that had been done several years earlier but much more professionally by a far more qualified person. The recent FH flight and the more Lunar focused interest at this time makes the idea more relevant than 10 years ago when I blogged it or 14 year ago when Dr. Walthelm published his work.

What makes it more relevant is the possibility of orbiting a hundred tons with one reusable F9, three hundred with one reusable FH, and both without expending an upper stage. The Blue Origin offerings won’t be far behind if the capability comes to pass. BFR payloads to the four digits. The expendable industry could be mostly extinct in a decade or so except for niche one offs. If there is any compelling reason to get tens of thousands of tons into Earth orbit, this could create an early profitable Lunar export.

This is the link to Dr. Walthelms concept.

This is my original post.  Comments are better than the post.

If I got the link wrong, this is the post.            Earth launch for heavy vehicles currently involves lifting a lot of propellant to lift a lot less vehicle to lift even less payload. One of the frequent criticisms of suborbital flight is that it only uses a small fraction of the energy required to reach orbit. While that argument has some serious validity issues, it would be nice to be able to pop up a suborbital vehicle and hand off a payload to something else that took it to orbit. Mass ratio required would drop by a factor of 5. While it would be nice, it may be a while before some magic tech makes it possible.

Tethers are the frequent solution suggested for making this happen. Unfortunately current tech seems to be that your suborbital vehicle would need to be traveling at mach 15 or so to match velocities with a rotovator. While this will be a major breakthrough when it takes place, it still requires a serious performance vehicle to make the rendezvous. The suborbital vehicle for that mission will have to be fairly aggressively designed if it is a single stage. The mass ratio is about half that of an orbital vehicle with serious TPS still required. It will have to ride the tether around for a few orbits to get home, or land far enough down range that getting home is another logistics problem. As better tethers become available, these problems will slowly get better until a true beanstalk becomes possible.

I’m not aware of any other feasible technologies for doing the job of an advanced rotovator.

With airless aerobraking propulsion, there is a possible solution.  A chunk of lunar LOX launched into a near earth reentry trajectory will be at over 11 km/sec as it makes a near approach 100 miles up. If one pound of this impacted a suborbital pop up vehicle that had no significant horizontal velocity it would deliver an impulse equivalent to an Isp of 1,100+. If that pound vaporized and rebounded at random from a heat shield, it would deliver equivalent of another Isp of 550. So each pound of lunar volatiles would have an effective ‘Isp’ of 1,650 while the suborbital vehicle is motionless earth relative. As the vehicle gathered momentum, ‘Isp’ would drop as a linear function of less impact velocity of each succeeding LLOXball. By the time the suborbital vehicle was pushed to orbit, ‘Isp’ would be down to about 460 or so. Lunar regolith aerogel was suggested for the airless aerobraking. If feasible, that would solve several problems with the concept.

It works out to about 1.5 times as much LLOX as vehicle to make the push to orbit. A one ton upper stage with heat shield would need about one and one half tons of LLOX impact to push it to orbit. The size vehicle it would take to get that one ton inert upper stage into position is in dispute by the various people that build actual hardware. The old V2 would have used 4 tons of vehicle and 9 tons of propellant. There are at least a half a dozen credible newspace companies that believe they can beat that with a vehicle that flies daily or more. The list of less credible is somewhat more extensive. The list of companies that can place a ton in orbit without help is fairly long, and fairly expensive.

If a firm can just match the old tech and get an upper stage boost from the moon, then a ton to orbit will be considerably cheaper than is currently possible. This is a 14 ton earth GLOW and 1.5 lunar volatiles per ton to LEO. Heavy lift is the field that would make this pay. A modern expendable design for this purpose would have a mass ratio of about 2.5 and a dry mass of less than 10%. A 3,000 ton GLOW (Saturn5 class) would get 900 tons in orbit in one shot with help from 1,350 tons of lunar volatiles in intersect trajectory.

If it becomes desirable to get a lot of large payloads from the earth surface into space, this might be one path for doing it. If a suborbital craft can fly often, then it could launch large payloads once a day as it phased with the moon launched trajectory paths. It would be cheaper to use lunar raw material to facilitate earth launch than to manufacture finished components on the moon for the short term of a few decades. If SPS became economically desirable, this is a technique that could help make it possible to launch millions of tons of earth built products into orbit.

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Research Papers I Wish I Could Con Someone Into Writing Part I: Lunar ISRU in the Age of RLVs

One of the things I’d love to do if I were successful enough at Altius to afford it would be to sponsor graduate-level research into space technology, business, economics, and policy topics that I’m interested in. Not just because I don’t have time to dig into these topics as deeply myself as I would like, but also because frankly there are lots of graduate students out there who have better analytical tools they could bring to bear than the crude ones I could come up with informally. I decided to share some of these ideas via a blog post in the hope that maybe I could either inspire someone in grad school who is looking for a research topic, or if not I could at least plant the seed for conversation on this blog. If someone is interested in doing one of these research topics, I’d love to do a review of the final paper when it comes out.

Topic One: Lunar ISRU Economics In The Age of RLVs
This is one that I often discuss with coblogger Chris Stelter on Twitter. There have been a lot of papers over the years looking at ISRU economics, but the vast majority, if not all of them, have made the assumption that launch costs are more or less static. I think I understand the usual reasons for doing so–either a) these papers are trying to recommend a policy change, and therefore are being compared against the status quo approaches of say government exploration missions using entirely earth-launched propellants, or b) at the time of the papers, RLVs weren’t taken very seriously, and the last thing they wanted to do was to make ISRU look less respectable by making it look like it depended on RLVs.

But now is probably a good time to start looking into what lunar ISRU economics look like if you assume RLVs can be successful in driving down launch costs in the foreseeable future. I’ve seen a lot of SpaceX fans recently who have made the argument that lunar or NEO ISRU is totally irrelevant because BFR costs are guaranteed to be so cheap that there’s no way lunar ISRU could possibly compete with it. I think this is… mildly overoptimistic, but one result of lunar ISRU studies that assume status quo earth-to-orbit launch costs (both for launching ISRU infrastructure, and as competition) is that the lunar ISRU price points they quote really do seem kind of high compared to potential RLV price points. I personally don’t think lunar ISRU is in as much trouble as all that, but I do think that since it is more likely that we’re at the dawn of the age of the RLV, that those interested in lunar ISRU economics should at least start looking as RLVs become available.

Some thoughts on approaches:

  • Launch costs are going to vary over time–even if gas and go RLVs happen in the foreseeable future, it’ll still take time to get there. So instead of treating launch costs as static, make a few scenarios where you make different assumptions about the shape of the launch cost vs. time “S-Curve”. How long does it take for significant reductions in $/kg to start appearing? How low can they realistically get before hitting diminishing returns? How steep is the slope of $/kg over time once that initial decrease starts creating new demand that creates virtuous cycles? The nice thing is that you can probably characterize these S-Curves with only a few parameters, and then you can come up with say at least three scenarios–a pessimistic one where RLVs are only mildly successful, and launch costs decrease slowly, hitting diminishing returns at a moderate price point, an optimistic one, where RLVs are very successful, and the transition is fast, with the point of diminishing returns being dramatically lower than current prices, and then a middle of the road S-Curve shape.
  • Assume that lunar ISRU developers are smart enough to leverage RLVs as they become available, so that launch of ISRU hardware can take advantage of the decreasing costs over time. For example–George Sowers was mentioning a recent CO School of Mines analysis that showed it was possible to extract water from the lunar poles for $500/kg of extracted water on the lunar surface. But he was assume a $35,000/kg delivery cost to the lunar surface for all the infrastructure.
  • It would be interesting to see analyses that reflect the idea that lunar ISRU developers might be able to leverage decreasing launch costs to also lower the exploration and development costs of their lunar ISRU capabilities.
  • It would be good to include scenarios for how hard lunar ISRU ends up being, ranging from scenarios where trying to crack oxygen out of the regolith is the best we can do, through lunar polar ice being legit, all the way through Warren Platts’ lunar aquifers scenario. My guess is that this could also be modeled by some sort of S-Curve as well, as there’s going to be a learning curve for developing lunar mining, that eventually snowballs, but then hits diminishing returns, but the timing, depth, and steepness of the curve could vary.
  • It would be cool to see analyses that assume different cislunar transportation architectures for getting lunar ISRU propellants back to LEO. Not just rocket only, but also architectures that use propellantless launch options (see my unfinished “Slings and Arrows” series), aerocapture, SEP transfer, nodes at different cislunar orbital locations (LEO, EML1/2, LLO, etc).
  • It would be interesting to see with these analyses where the equillibrium point ends up being for lunar ISRU vs RLV-earth-launched propellants under different assumptions. I could see some cases (optimistic RLVs, pessimistic lunar resource difficulty, lame approaches to cislunar transportation) where lunar ISRU isn’t even competitive on the lunar surface, while there may be other scenarios, where lunar ISRU wins hands down even in LEO. But it would be interesting to see patterns and what assumptions lead to which outcomes.

Anyhow, I just wanted to seed the thought. I’ll probably turn this into a series for other research topics I’d like to see others write, but I wanted to throw this one out there.

Posted in BFR, ISRU, Lunar Commerce, Lunar Exploration and Development, Research Papers I'd Like to Con Others Into Writing, Space Development | 21 Comments

Flyback Shrouds

Seeing the picture of the SpaceX shroud floating in the water, it struck me how much it resembled the bottom half of certain lifting bodies. Then it struck me that this thought had been around before, whether it had been a passing thought, or a hint of memory of a past conversation.

My current thought is that the shroud inflates an upper body after separation and deploys a couple of vertical tails. Very fluffy flying reentry for a controlled glide to recovery. It seems possible that a very light propulsion unit of about 100-200 hp could extend the glide to an RTLS. Or possibly a aerial tow RTLS.

Does anyone know if this is a new (if not unique) thought or just a forgotten memory of a previous discussion?

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Random Thoughts: A Now Rather Cold Take on BFR

When Elon gave his update on BFR at the IAC conference in Australia, I was originally going to post some thoughts right away1. But with Falcon Heavy’s maiden launch attempt coming up tomorrow, I realized I still hadn’t collected my thoughts about BFR into one place, instead of leaving them scattered over two dozen twitter arguments with Chris and others. I’ve had a lot of thoughts since the original announcement, but I wanted to share five thoughts that I had at the time that I still feel pretty strongly about:

  1. More Reasonable Size (Though Still Probably Too Big): I liked that Elon shrunk the size of BFR to something slightly less insane than ITS (a 50% drop from 300mT to 150mT). I still think he’s going way too big for any realistic markets near or medium term markets, but it’s a step in the right direction. I’m not convinced you need anything bigger than ~30-40mT to LEO to do Mars exploration and settlement, and you definitely don’t need anything that big to service near-term and future markets.
  2. Replacing Falcon 9, Falcon Heavy and Dragon with BFR/BFS: This was actually my favorite part of the plan in theory. In theory replacing the semi-expendable Falcon 9 and Falcon Heavy with a fully-reusable, and in-space refuelable launch vehicle would be a great idea. Especially one that was a single-stick, not crazy high aspect-ratio vehicle. And once you have that, and have the upper stage reliability up high enough, having an integral crew/passenger capability without needing a separate capsule could be a really powerful combination. Getting to high flight rate reusability is far more important for affordable deep space transport than getting to gargantuan rocket size. Something more modestly sized (say in the 30-40mT fully reusable range) would’ve been a much smaller leap, and I think would’ve much better taken advantage of the best part of Elon’s updated plan.
  3. BFR Leaves Open Room for Competition:At 150mT, BFR would be flying mostly empty on most flights for the foreseeable future. It would only really replace Falcon 9, Falcon Heavy, and Dragon if nobody else succeeds at doing a fully-reusable vehicle in a more sane scale. While it may be possible that a BFR sized fully-reusable launch vehicle might have much lower $/kg when flying completely full than a smaller sized fully-reusable vehicle using similar design architecture and technology choices, if BFR is flying mostly empty for most realistic near-term missions (satellite launch, ISS crew/cargo, etc), the actual cost to fly a realistic payload will probably be cheaper on a more right-sized vehicle. Personally, I think there’s a huge potential here for someone who wants to make a 1-10mT to LEO full RLV. While the $/kg might not be as good as a fully-loaded BFR or fully-reusable New Glenn/New Armstrong, the $/mission for most realistic near-term missions would likely be lower. I really hope someone else is able to raise money and execute on a small to medium RLV, I really don’t want to have to go back to launch vehicles for my next startup.
  4. Skeptical about Suborbital Point to Point: If you project BFR economics out to the point where it really hits some low multiple of the propellant costs, it theoretically could be competitive for some long-range travel. I just have a hard time seeing a rocket-based system with that high of performance and that razor thin of margins ever getting within spitting distance of the reliability of jet aircraft, especially within the foreseeable future. There are just so many technical and non-technical challenges for this market to make sense, and I think a lot of them are exacerbated by how big BFR is.
  5. What About Space Tourism? While I’m really skeptical about how realistic the suborbital point-to-point market for BFR, I’m kind of surprised Elon didn’t propose space tourism as a market. After all, if BFR can really keep 100+ people comfortable for a 6+ month Mars mission, you’d think they could easily handle 100 people for a 1-2 week stay in LEO. Even without space hotels as a destination, if he can really get down to a $200k/person Mars ticket using 5 launches, he should be able to get down to a $40k/person ticket for a two week space trip. If he was going to a space hotel and could pack people in as tightly as they were suggesting for BFR point-to-point suborbital flights, he could probably get the price for a LEO vacation down below $10k. While there are legitimate questions about how much market there is for space tourism at $20M+ per seat, is there really any doubt that there’d be a market for space tourism if it really cost only $10-20k per person for a 1-2 week LEO cruise?

Those were the five things that hit me the most. While I think BFR is an improvement over the original ITS plan, I think it still leaves a big opening for a serious competitor that didn’t feel the need to get into rocket size competitions with Elon and Jeff2.

Posted in BFR, Blue Origin, Random Thoughts, SpaceX | 49 Comments

AAS Paper Review: Practical Methodologies For Low Delta-V Penalty, On-Time Departures To Arbitrary Interplanetary Destinations From A Medium-Inclination Low-Earth Orbit Depot

I’d like to share a technical paper about propellant depots and interplanetary mission orbital dynamics that I helped co-author this past year, with the help of two of my astrogator friends1, Mike Loucks and John Carrico of Space Exploration Engineering and The Astrogators Guild blog.

By way of preface, this is a paper that Mike and I have been meaning to write for almost five years now2 as a rebuttal to some anti-LEO depot arguments that had started to come out back in the 2010 timeframe. You see, back when the FY2011 NASA Budget came out, those of us who had been advocating LEO propellant depots as a source-agnostic way of driving innovations in low-cost launch and Lunar/NEO ISRU thought we had finally won the day. Constellation had been cancelled. The president was proposing having NASA invest heavily in technology demonstrations for reducing to practice ideas like depots.

But then the idea of LEO depots started taking a lot of flack from many directions. Probably one of the most effective critiques of LEO propellant depots came from a NASA Flight Dynamics Office out of JSC who pointed out some orbital dynamics challenges of using LEO depots for doing interplanetary missions to places like asteroids. While I think the issues were raised in good faith–there are some legitimate challenges that LEO depots need to overcome–groups at NASA that didn’t want competition for their Monster Rocket used these arguments to “prove” that LEO depots weren’t really that useful after all, because you see, they weren’t useful for performing the asteroid missions NASA was now planning. It probably didn’t help that a certain one of its parent companies informed ULA’s depot advocates in no uncertain terms that depot was now a four-letter word that could be severely career limiting to use3.

The AAS Paper
Before I get into the orbital dynamics issue that was raised, and the solution we present in the paper, why don’t I share a link to the paper itself for those of you who would like to cut to the chase: AAS 17-696. This was presented at the AAS/AIAA Astrodynamics Specialist Conference which was held August 20-24, 2017 in Stevenson, Washington, U.S.A. If you’re interested, hard copies of this and the other presentations will soon be available in Volume 162 of Advances in the Astronautical Sciences. Fortunately AAS was fine with me sharing a copy of this on the blog so long as I gave proper credit.

The “Show Stopper”
So, unless you’re a real space nerd and happen to already know the answer, you’re probably wondering what the orbital dynamics issue was that NASA used as an excuse to ignore depots over the past five years. The tl;dr version of the issue is that while you can launch a LEO propellant depot in a way that lines up well for one specific interplanetary departure opportunity, it’s almost guaranteed to not be aligned well for most subsequent interplanetary missions you’d like to perform.

The longer version is driven by the concept of nodal precession. You see, because our planet spins, it’s a little… round about the middle. This bulge causes a “J2 perturbation” to orbits4, that basically causes the orbit plane to slowly precess around the earth’s rotational axis. I can’t remember exact numbers off the top of my head, but I think we’re talking 5-7 degrees per day for an ISS-like depot orbit. I could geek out on more facts about nodal precession, but here’s why that matters–once you launch a depot into LEO, you’ve established an orbital plane for that depot. That plane will precess over time in a very predictable way. The problem is that for a given interplanetary departure window, you need to leave earth on a specific departure vector (called the departure asymptote)5, and if the plane of your LEO parking orbit doesn’t intercept that departure asymptote vector at your departure date, you can’t do a coplanar one-burn departure, which means you have to deal with a very painful plane-change delta-V penalty that gets rapidly more painful the further the misalignment between your departure vector and your orbital plane. Another problem is that for weird destinations like some NEOs, the required departure asymptote is pointing off in a direction far from the equator–far enough that it might be higher than the inclination of a reasonable LEO depot, which means that you would never get a one-burn coplanar departure opportunity that didn’t require a debilitating plane change maneuver.

The good news is that since nodal precession is pretty easy to model, you can definitely place your depot into an orbital plane that will drift into alignment with a single departure opportunity. The problem is that the odds of it lining up with any given future arbitrary departure opportunity is pretty poor. Depending on how short the window is, and it tends to be really short for many NEOs, your odds might be less than 25% of having your depot in the right place at the right time. The odds of alignment are better if you’re talking planetary departures, as those tend to have longer windows at lower declinations (the angle from the equatorial plane to the departure asymptote vector), but still nowhere near the 100% you’d probably prefer for a critical piece of space infrastructure.

Ground launches don’t have the same problem because unlike an orbital plane that precesses very slowly, a ground launch site rotates with the earth 360 degrees every 24hrs. And a ground site can easily launch into a parking orbit with any inclination higher than the latitude of the site. Basically, you can pick the parking orbit of your departure to line up with your target every time.

I’m glossing over some details, but it all seems pretty damning when you think of it like that. Why build an expensive piece of infrastructure that you can’t count on being usable for any given mission?

Previous Proposed Solutions
Fortunately, there are some potential solutions that have been proposed in the past that still allow you to use LEO depots but get around this problem6. One option would be to have multiple depots instead of just one. If you have somewhere around 4-6 evenly-spaced depots, you should be able to always have a depot that will be aligned with a given destination at the right time, and you’ll know far enough in advance that you can logistically schedule different missions out of different depots. The problem is that this probably only makes sense if you have a really high flight rate. Another option proposed is to phase the depot orbit between missions–you can change your nodal precession rate by raising your apogee or lowering your perigee. If you know where you need to be far enough in advance, you don’t have to tweak your orbit too far to have it either precess faster or slower so it ends up in the right place at the right time. The problem with this approach is that it only works with really low flight rates, since it can take a long time to phase into the right orbit, especially if radiation or drag limits prevent you from changing your apogee or perigee too much. And neither of these solutions solve the problem if your departure declination is higher than the inclination of of your orbit, because the only solution at that point would be to do a plane change for your depot to get into a higher inclination orbit–and those are really painful maneuvers from a delta-V standpoint.

3-Burn Departures
While both of those solutions kind of work, Mike Loucks and I came up with a potentially better solution based on a MXER tether paper by someone who many Selenian Boondocks readers might recognize. You see, the best place to put a MXER tether is in equatorial orbit, because that maximizes the frequency of launch opportunities you have. But as I mentioned above, if the declination of the departure vector is higher than the inclination of your orbit, you’ll never have a coplanar one-burn departure. So what was Kirk’s solution? Use a 3-burn trajectory!

But first I need to explain something about departure orbits. Interplanetary departure orbits are by definition hyperbolic trajectories. And hyperbolic trajectories don’t behave quite like circular or elliptical ones. With a circular orbit, if you do an instantaneous (impulsive) burn, that point in your orbit where you did the burn becomes the perigee of an eliptical orbit, and the apogee will occur on a line that goes from that perigee through the center of the planet (that line is called the line of apsides if you’re wondering). So long as you’re still in an elliptical orbit this will always be the case. If you hit exactly escape velocity (i.e. have no excess velocity above escape), you’re in a parabolic orbit, which will point asymptotically as it approaches infinity in that same direction (i.e. parallel with the line between your perigee and the center of the earth). But as soon as you go a little faster, you’re in a hyperbolic trajectory, and the trajectory you end up asymptotically approach at infinity no longer aligns with that same line–the angle that a hyperbolic orbit has relative to that line between the perigee and the departure asymptote is I believe called the turning angle. And the turning angle gets bigger and bigger the faster you’re going relative to escape velocity. Combine that with the fact that any plane that is coplanar with the desired departure asymptote can allow a hyperbolic departure, and you get a famous drawing like that in the astrodynamics book by Bate, Mueller, and White (Figure 2 from both of the referenced papers) shown below:

Hyperbolic Departures (credit: Bate, Mueller, and White)

What you may notice is that there’s actually a ring, or “locus” of injection points (aka locus of periapses) that all allow you to get to the same departure asymptote. This ring, which is centered on the axis formed by the desired departure asymptote gets wider as the required injection velocity increases (higher C3), and narrower as it decreases.

Ok, so how does this enable a 3-burn departure that gets around the constraints described in the earlier section?

In order to do a coplanar departure without penalties, you need your perigee to be on that locus of injection points at the time of the final departure burn, you need the plane to be coplanar with the departure asymptote, and you need to be going in the right direction in your orbit. You can meet those three criteria if your LEO depot orbit plane happens to line up with the departure asymptote at the right time, but it turns out there’s a 3-burn trick you can do that allows you to meet those criteria for your final burn so long as your depot’s orbital plane ever crosses through any point on that locus of periapses at a point prior to your desired launch window.

Here’s how:

  1. At any time your orbit crosses through that locus of injection points, you do a large apogee raising burn that has an orbital period timed so that you return to perigee at the exact time you want to do the interplanetary departure burn7. This solves having your perigee on the right locus of injection points at the right time even if your LEO depot orbit has long since precessed out of optimal alignment. This burn also is not wasted as all of the energy you put into raising your apogee has come back as kinetic energy when you’re back at perigee for the final burn.
  2. Once you’re at apogee you’ll probably need to do a plane change maneuver to rotate your plane so that when you get back down to perigee your plane is coplanar with the desired departure asymptote, and you’re headed in the right direction. Since plane change costs are proportional to your velocity at the point in your orbit that you do them, they’re cheapest at apogee, especially for a high apogee near escape velocity.
  3. When you drop down to the perigee, you’re now lined up for your third and final burn which sends you to your destination.

If you’re having a hard time visualizing it, our AAS paper has a bunch of illustrations of what the trajectory looks like, including some practical mission examples, including an excellent acid test case provided by Josh Hopkins of Lockheed Martin (a mission to NEO 2007 XB23, which has a really crazy departure declination of -72 degrees).

Now there are all sorts of subtle nuances that can complicate this or make things better. For instance, because of how vectors add, you almost certainly want to split your plane change up between burns one, two, and three, because that’ll lower the overall penalty. Also, if your apogee is too high, you might start running into lunar perturbations that would have to be compensated for. Also, you might want to lower your perigee when you’re at apogee, to get a little more boost from the Oberth effect. Also, while your nodal precession rate drops off dramatically for a highly elliptical orbit, it’s not exactly zero. But all of these perturbations can be modeled and planned for when designing your 3-burn departure trajectory.

It’s worth mentioning that you can do this process in reverse to rendezvous with a LEO depot when coming in from an arbitrary interplanetary trajectory8.

While this is more complex than a single-burn departure, look what this does for you:

  1. You now can always hit your desired departure window even if your depot orbit itself is very misaligned with the asymptote.
  2. You can hit a departure asymptote even if the declination is higher than your inclination–it now just has to be lower than the sum of your inclination and turning angle, meaning that the higher the required departure velocity, the lower the inclination of your depot can be to hit a given departure declination. If your departure C3 is >16km^2/s^2, you can hit any departure declination from an ISS-like 51.6 degree depot orbit.
  3. It can also allow you to do missions that would require more propellant than your depot can handle. Basically, you can launch one tanker into this highly elliptical parking orbit that has your perigee on the desired injection point, long in advance of your desired departure window. The nodal precession rate of this highly elliptical orbit will be almost zero, so the depot orbit will rotate into alignment with it approximately once every 2-2.5 months. Each time it aligns with this parking orbit with the tanker in it, you can launch another tanker to rendezvous with, and add propellant to the first one, until it’s all the way full. Once that’s done, you can expend, or better yet aerobrake these depleted tankers back into LEO for reuse. Then when you’re at your last perigee before departure, you can launch the actual mission stack into the highly elliptical phasing orbit, rendezvous with the now full tanker, transfer propellant from the tanker, and then do your plane change burn at apogee, and your departure burn when you’re back down to perigee. In this way, or with variations on the theme, you can do really impressive missions using relatively modest sized depots9.
  4. And you get all of these benefits without having to do large numbers of depots and without having to move the depot, so you could theoretically park the depot in something like a resonant orbit that makes refueling logistics much easier10.

There are a few drawbacks or complexities, but they’re mostly minor:

  1. You do get two or more extra passes through the Van Allen Belt per departure mission. Not the best thing in the world, but not the end of the world either.
  2. You do still have some plane change penalty11, unless you can perform the first burn at a time when your LEO depot orbit is coplanar with the the departure asymptote12.
  3. You add a non-trivial amount of time to the mission, possibly on the order of weeks.
  4. You now have to do at least two burns a very long time after the first burn. Most current rocket stages are only designed for mission durations of 14hrs or less. Which means if you don’t have a long-lived stage (like ULA’s planned ACES stage), you probably need to do the second and third burn using something storable, which does cause a slight performance hit. In most cases the first burn is the biggest of the three though, so you still get some benefit from having your higher performance stage even if you have to have a kick stage of sorts for the final departure.
  5. You have more mission complexity and three important burns rather than just one for departure. But the nice thing is if either the first or second burn fails, you can probably abort the mission.

One “turning lemons into lemonade” advantage of this approach is that you get more time to check out your vehicle before its committed to interplanetary space. Once you’ve done that final departure burn, most systems really have no way to abort if something goes wrong. And with the bathtub reliability curve most complex systems have, it might actually be better to have an extra 2-3 weeks of checkout time during the elliptical phasing orbit to make sure everything is really ready for commit, with the option of aborting the mission if its not. Another side benefit of the elliptical orbit is that they have much lower (likely 10x lower) cryogenic boiloff rates, since you spend more time far away from nice warm planetary bodies. And you spend most of your time away from LEO where the MMOD environment is much, much better, which means that if you want to build up a mission stack over time (in a similar manner to the tanker concept discussed above), you can do so with less worry of MMOD damage to your mission stack while it waits than if you built it up in LEO.

While there’s still a lot of work to better evaluate optimizations and tradeoffs, and to explore various architectures enabled by this 3-burn departure (or arrival) method, we were able to identify and demonstrate a method that allows you to reuse a LEO depot for multiple missions, in a way that can always hit the desired departures at minimum penalty, even in spite of the previously raised issues due to LEO depot nodal precession. I wish we had been able to present this four or five years ago when we first discovered the solution. Maybe that would’ve at least dispelled the notion that orbital dynamics are a show-stopper for LEO propellant depots.

Posted in Orbital Dynamics, Propellant Depots, Space Transportation, ULA | 12 Comments