Pictured above is Robert Farquhar's route between EML2 and LEO. It's time reversible so it could be to or from EML2.
A .15 km/s burn at EML2 will drop a spacecraft to a perilune 111 km from the moon's surface. At this perilune the spacecraft is traveling nearly lunar escape velocity with regard to the moon and so enjoys an Oberth benefit. A .19 km/s perilune burn suffices to send the spacecraft earthward to a perigee deep in earth's gravity.
At perigee the spacecraft is traveling about 10.8 km/s, just a hair under earth escape. A burn at this perigee enjoys a huge Oberth benefit. A .6 km/s burn would suffice for Trans Mars Injection (TMI). So delta V from EML2 to TMI is (.15 + .19 + .6) km/s. I will round .94 km/s up to 1 km/s to give a little margin and also 1 is an easier number to type.
After TMI the EDS as well as it's payload is moving 11.5 km/s. To reuse the EDS we would need to return it to EML2.
Farquhar notes the trip from perilune to perigee takes about 140 hours. In that time the moon will advance 76º and the space craft 180º. So in my shotgun orbit simulator I set the perigee 104º ahead of the moon. My first try had pellets ranging from 10.7 to 10.9 km/s and then I'd narrow the blast to the pellets coming closest to the moon. After a few iterations I arrived at a perigee velocity of about 10.85 km/s. This gives an apogee of about 396,000 km and a period close to 2/5 that of the moon. After 50 days, the pellets return to a near moon fly by:
Thus braking about .6 km/s drop the EDS hyperbolic path to a trajectory where it will do a near moon fly-by after 50 days. At the near moon fly by it can do a .14 km/s burn for lunar capture. Then when it reaches an apolune near EML2, a .19 km/s burn to park at EML2.
Thus the EDS' delta V for returning to EML2 will be about 1 km/s.
This page still a work in progress, I'm getting good comments and info from a NASA spaceflight thread. Cryogenic boil off was an issue raised in that thread. A sixty day round trip goes well beyond what present hydrogen/oxygen upper stages do.
Revisiting Kirk Sorensen's EML2 thread I noticed he had posted a Farquhar illustration suggesting reusable booster stages could be returned to EML2!
The United Launch Alliance has done work on hydrogen/oxygen upper stages that could do longer missions. See Advanced Cryogenic Evolved Stage (ACES). Cyrogenic boil off might be mitigated by Multi Layer Insulation (MLI). Another cooling device is a Thermodynamic Vent System (TVS). Those who live in the southwest are familiar with "swamp coolers" where water soaked pads cool by evaporation. In a similar fashion hydrogen boil-off can be used to cool the cryogens. The hydrogen boil off can be vented in a specific directions and used for station keeping or attitude control.
Besides these passive thermal control systems the ACES might also utilize a two stage turboBrayton cryocooler.
"This design was based on the Creare NICMOS cooler that has been flying on the Hubble Space Telescope for the last ~4 years. The turboBrayton cycle uses GHe as the working fluid and this cooled gas can be easily distributed to the loads (i.e. the 22K and 95K shields). The ACES cryocooler configuration, shown in Figure 3-1, has 3 compressors in series and 2 expansion turbines in parallel, one for the 22K load, and one for the 95K load".
In this ULA pdf an ACES 41 propellant tanker has 5 tonnes dry mass and 41 tonnes propellent. I will be much more conservative in my hypothetical reusable EDS. A Centaur has 2.25 tonnes dry mass, 21 tonnes propellent and 99.2 kilo newtons. I will use the same but boost the dry mass to 5 tonnes for MLI, cryocooling, solar arrays, etc.
Specs for Hop's EDS
5 tonnes dry mass
21 tonnes hydrogen/oxygen
99.2 kilo newtons thrust
After the EDS sends the payload on its way, it will need 1 km/s of propellent of delta V to return to EML2. Exhaust velocity of hydrogen and oxygen is about 4.4 km/s. Exp(1/4.4) - 1 is about .255. To get back the EDS' 5 tonnes of dry mass we'd need 1.3 tonnes of propellent.
So for the first leg of the trip we have (21 - 1.3) tonnes of propellent or 19.7 tonnes. The first leg is also a 1 km/s delta V budget. With a 1 km/s delta V budget, 19.7 tonnes of propellent can do 19.7tonnes/.255. That's about 77 tonnes. But recall 6.3 tonnes is EDS dry mass plus propellent for the return trip. That's (77 - 6.3) tonnes of propellent available for payload. Let's call that 70 tonnes.
This little EDS could impart Trans Mars Insertion (TMI) to 70 tonne payload. Two of these EDS stages could send a 140 tonne payload on its way to Mars. Wilson and Clarke imagine a Mars Transfer Vehicle (MTV) of 130 tonnes.
Of the MTVs 130 tonnes, about 60 tonnes is propellent and consumables. If propellent, water and air are available from an asteroid or lunar volatiles, it would only be necessary to send the MTV's 70 tonne dry mass to EML2.
Wilson and Clarke also call for two EDS stages (they call them TMS -- Trans Mars Stages). Their stages are 110 tonnes and not reusable.
130 + 2*110 = 350. 350 tonnes to LEO for each (non reusable) conventional MTV. Vs 70 tonnes to LEO for an MTV that relies on extra terrestrial propellent and consumables. And an MTV departing from and returning to EML2 would have a much lower delta V budget. Making the MTV reusable would be much more doable.
The EDS would zoom through the perigee neighborhood very quickly. Would it have enough time to do the burns and enjoy an Oberth benefit?
The EDS and payload would spend about 54 minutes in the shaded region above.
A 70 tonne payload plus a 26 tonne EDS total 96 tonnes. The thrust of the engine is 99.2 kilonewtons. Acceleration is newtons/kilograms. 96/99.2 is ~.96. .96 meters/second^2 is about a tenth of a g.
Delta V imparted is acceleration * time of burn. Recall the perigee burn is about .6 km/s or 600 meters/second. We solve for t.
a * t = v
.96 m/s^2 * t = 600 m/s
t = 600/.96 seconds = ~620 seconds, a little over 10 minutes. The ten minute neighborhood just preceding perigee is all close to 10.8 km/s.
After separating from payload, the EDS and it's return propellent mass 6.3 tonnes. 99.2 kilonewtons divided by 6.3 tonnes is 15.75 meters/second^2 or nearly two g's. The deceleration burn to brake the hyperbolic orbit to an elliptical capture orbit would take about 40 seconds.
Near Earth Asteroid Retrieval
The Near Earth Asteroid retrieval described in the Keck Report uses xenon as a propellent. The exhaust velocity would be 30 km/s. What possible use could an EDS with a measly 4.4 km/s exhaust velocity be for such a vehicle?
Along with xenon's high exhaust velocity comes very low thrust. It would take nearly two years to spiral from Low Earth Orbit (LEO) to escape velocity. A good part of that long spiral would be spent in the Van Allen Belts. Low Earth Orbit also has a relatively high debris density.
Low thrust rockets don't enjoy any Oberth benefit. So the spiral from LEO to C3=0 would take about 7 km/s. Recall the exhaust velocity of the xenon rockets is around 30 km/s. Exp(7/30) - 1 is .26. Using an EDS would leave the asteroid fetcher with about 33% more xenon.
Many NEAs are much closer than Mars in terms of delta V. So perigee burn would be much less than .6 km/s for TMI, probably more often in the neighborhood of .2 or .3 km/s.
First, a slightly OT and stupid question: What is meant by "pellets" here? Tiny pebbles of extracted lunar ice?
ReplyDeleteSecond, concerning the boil-off problem. A guy named Doug Plata suggests that water be transported from lunar craters to low lunar orbit and that fuel be produced only on order. As late as production capacity allows. Is this self evident, or undoable?
See his ideas at (page 5 on):
http://www.cislunarone.com/
I have a toy that blast 11 "shot gun" pellets over a range of velocities. http://clowder.net/hop/railroad/OrbSim.html -- that makes it easier for me to find routes by trial and error.
ReplyDeleteDoug Plata and I are on the same page in many respects. 60 days from leaving the EML2 depot to EML2 return may pushing hydrogen boil off although it's possible to mitigate with MLI (Multi Layer Insulation) and other devices. When I have time I will flesh out this EDS roughly basing it on a Centaur upper stage.
I've invented a new "astrogeographical realm" of the Solar System, the idea behind it being that we limit ourselves unnecessarily by adhering to labels like "moon," "Mars," and "asteroid." I've begun to write about Terralune (as I call this region) on a blog. I've been enjoying your blog immensely and wonder whether you would care to have a look at my blog. I suspect that, if my blog contains glaring errors, then you would be able to locate them. Here's the URL:
ReplyDeletehttp://dsfpterralune.blogspot.com/
I hope that you will find this concept to be of interest.
dsfp
Thanks for the informative post. However, I'm not so sure doing two Oberth burns would work. I tried the calculation and concluded that you would be better off just doing a single burn at Earth because its higher escape velocity would provide a larger Oberth boost:
ReplyDeleteMath needed for 5-week flight from Earth to Mars.
http://www.orbiter-forum.com/showthread.php?p=446531&postcount=38
But what might work is, for departures from Earth, to aim first for the Moon to get a gravitational slingshot effect, but so that it swings around to head back to Earth. Then use the Oberth effect at the Earth.
Bob Clark
I am working on a hybrid chemical/NEP Centaur here;
ReplyDeletehttp://yellowdragonblog.com/category/small-fission-reactorchemical-stage-hybrids/
the challenge would be to design a small fission reactor that could while inert withstand cryogenic fluids.
the waste heat is perhaps more important then the extra power from the radiator and the xenon gas ullage in the Centaur tanks, as it keeps the Centaur and payload warm during long Lunar nights and during outer planet missions
Bob, to exploit the potential energy of a high orbit you need to do a braking burn to drop the perigee deep into earth's gravity well. Braking burn from EML1 is around .7 km/s.
ReplyDeleteEML2 has even more potential energy than EML1. Under normal circumstances the braking burn would take more than .7 km/s. But Farquhar's clever use of the moon's gravity well cuts braking expense to .3 km/s.
Idle thought: You calculate a 10 minute burn at perigee for the 70-ton payload and the stage, but that's with a single 99 kN RL-10 equivalent. With three such engines, you can chop that down to three minutes, and still only see 0.3 G. That'd mean you could do the burn, drop the payload, and re-orient for the stage to do its own slow-down burn without needing to leave the lunar area--you've got 54 minutes after all. The reusable departure stage need only be on the hyperbolic trajectory long enough to drop the payload.
ReplyDelete