Ok, before I run off to work today, I wanted to follow-up on my comments last night regarding reusable lunar transportation systems.
Propulsive Braking or Aerobraking?
One of the questions that comes up a lot regarding reusable LEO-LUNO or LEO-L1 tug is how do you actually intend to get it back to LEO. The main options are to do it propulsively (ie by using its engines to decelerate and recircularize in LEO), or to use the earth’s upper atmosphere to slow down sufficiently, or to use a combination of both.
Propulsive braking is the easiest to do, has the least unknowns involved, requires the least beefing up of the tug, and requires the least new development work. On the other hand, it requires a huge amount of propellant to work correctly. This is due to the fact that with nothing to brake against other than your hot flamey stuff, you end up spending exactly as much propellant (to a first order approximation) getting back from L1 as you did getting out to L1 in the first place. I ran the numbers last night for a tug using LOX/IPA, LOX/Propane, and LOX/LH2 in order to take 4000lbs on an LEO to L1 and back round trip, and for taking the maximum amount of cargo to L1 with no cargo on the return loop. I assumed a roughly 3.7km/s Delta-V requirement for getting from LEO to L1. The good news is that even for LOX/IPA (which I assumed only had an Isp of 340s or so using space rated engines), the required stage fractions were well within what has been historically feasible (roughly 10% fuel and a few percent payload). Problem was that the stage in LEO required nearly 200klb of fuel in LEO to take 4000lb of crew or cargo on a round trip to L1 and back. For the LH2 stage, this dropped to only ~45klb of fuel, which is a lot more palatable. LOX/propane was in the middle with ~87klb of fuel required. The interesting thing though was that if you assumed a one-way delivery with the tug returning empty, the payload mass shot up to about 12000lb for the LOX/IPA, 11000lb with the LOX/Propane, and about 9000lb for the LOX/LH2 stage. The short and long of this analysis is that purely propulsive braking is likely quite expensive, but perfectly technically doable. And as Rand and other would likely point out, if you’re flying that many small flights, you’re going to see the cost per pound in orbit go way down along the way, since you can amortize your fixed costs and development costs over more flights.
Full or “100%” Aerobraking is both more tempting and trickier. With full aerobraking, you only need about 1km/s of Delta-V to go from L1 to an ellptical orbit intersecting the earth’s upper atmosphere, which does the rest of the job. But as any Heilein fan will point out, TANSTAAFL! The problem is that hitting just the right part of the atmosphere to slow down in a single pass without using any extra fuel is very, very difficult. For some background, since atmospheric heating varies strongly with gas density, you really want to do your aerobraking higher up in the atmosphere to keep the heat load down. However, particularly at the altitudes of interest, there’s a big problem–the atmosphere doesn’t stay put! As various factors such as solar radiation and the solar wind change, they cause the upper bounds of the atmosphere to contract and expand. I don’t have a good handle on what kind of timescales we’re talking about (my guess would be hours to a day or so for a fairly large change), but they’re likely fast enough to be a problem. For a vehicle designed for 100% aerobraking, you’re in a bit of a pickle, particularly if you have passengers. If you undershoot, you’ll skip off and it’ll be days or weeks before you can get yourself back into LEO (which could be a very bad day). If you overshoot, you’ll deorbit and have to land (if your vehicle can take that kind of extra heat input over and above the aerobraking). The problem is that with all the unknowns involved, it’s really hard to do this right. One solution might be to get much better and more frequent measurements of the part of the atmosphere of interest, either using some sort of sensors on some satellites, or using sounding rockets or some other means. If you could know the atmospheric properties in the target area with enough accuracy, it would be a lot easier to do a last minute course correction, and slide in right in the sweet spot.
The other option is to cheat and take the best of both worlds, and use partial aerobraking. What I mean by partial aerobraking is that of the 2.7km/s of delta V needed for circularizing into LEO, you only have the atmosphere provide part of that, say 1.5-2.5km/s. By keeping enough reserve fuel on board, you can afford to aim a little higher up in the atmosphere. Basically, you can bias your errors so that you tend to err on the side of less delta-V provided by the atmosphere, and hence more propulsive braking in order to reduce the odds of accidentally deorbiting yourself. I’m pretty sure that some combination of better information, lots of practice actually doing aerobraking, and a decent amount of reserve propellant should make a huge difference in the safety and reliability of such a scheme. And even with only about 75% aerobraking (ie having atmospheric drag contribute 2km/s out of the 2.7km/s of Delta-V), the mass savings are enormous. The IPA fueled tug drops from nearly 225klb wet mass in LEO to only about 55klb. The Propane fueld one drops from 87klb to about 37klb, and the LH2 one drops from about 55klb to about 26klb (with 4klb of that being cargo). Since you’re not on quite as steep of a section of the Delta-V versus mass ratio curve however, your one-way only cargo only goes up to about ~5500-6000lb. End result is however that you end up spending less than half as much propellant mass in LEO for given payload in L1 if you can do at least partial aerobraking.
And since you’re only trying to bleed off 2km/s, have a very favorable ballistic coefficient (ie you’re very fluffy), and are doing most of your decelerating in the upper atmosphere, the heat shield may be a lot easier to work with. I slated for a heat shield in each of those cases that was about 5% of the loaded mass of the vehicle (about 20-30% of the aerobraking mass however), which is probably reasonable.
So as you can see, there are tradeoffs, but once we can get in the practice of doing at least partial aerobraking (and a series of tech demos of such would go a long way to proving the idea out), it has some strong advantages.
Ok, I’ve ran out of time again, so I’m going to have to pick this up again later on today.
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