Saturday, December 14, 2013

Arrgh! It's not the cost of the fuel

"What's the cost of propellant from earth vs getting it from the moon?" always comes up in discussions of lunar water. Or the cost of near earth asteroid propellant vs earth propellant.

Propellant is cheap, typically a small percentage of spacecraft expense. Spaceflight is expensive because vehicles are disposable. How much would a plane ticket cost if a 747 were thrown away each trip?

Well, how come we don't re-use our spaceships? It's due to constraints imposed by the rocket equation.

As delta-V budget  climbs, dry mass fraction shrinks. We can't eliminate engine or payload mass. We cut dry mass by making walls thinner and structure more tenuous.



Thinner walls mean fragility. Designing upper stages is like designing egg shells.

Upper stages are like cascarónes, confetti eggs. While cascarónes are fragile by design, upper stages are fragile due to the constraints imposed by the rocket equation and high delta-V budgets. An upper stage plunging into the atmosphere is like a cascarón plunging onto a friend or relative's head. But the conditions of re-entering earth's atmosphere at 8 kilometers/second are much more extreme than the back of her mom's head.


Given propellant depots at LEO, GEO, and EML1 or 2, ferries between orbits would have delta V budgets of 4 km/s or less. Moving between orbits, they don't have to endure re-entry. Much less difficult mass fractions and eliminating the extreme conditions of re-entry make re-usable ferries doable.

But how would these ferries by fueled? Tankers from earth would have a delta V budget of at least 9.5 km/s. If the tankers are throw-away, it is simpler and cheaper to just use the tanker to deliver the payload rather than fueling a ferry to deliver a payload.

However if the fuel source is the moon's surface or an asteroid at EML1 or 2, the tankers have lower delta V budgets and thus much less difficult mass fractions. Given reusable tankers to supply fuel, reusable ferries make sense.

Moreover, given propellant in LEO, an upper stage returning to the earth's surface doesn't have to re-enter at 8 km/s. Given propellant in LEO it can refuel and shed some of it's orbital velocity via reaction mass instead of aerobraking. Eliminating the 8 km/s re-entry makes re-use of upper stages much less difficult.

So it's completely missing the point to compare the price of earthly propellant delivered to the moon's surface vs propellant mined on the moon. The object isn't to get water on the moon's surface. The object is to get propellant at various locations in cislunar space so the delta V budgets can be busted into manageable chunks.

By breaking the tyranny of the rocket equation, reusable ships become possible. Given easily reusable space ships, the economies of spaceflight are completely changed. This is the potential of lunar (or NEO) water.

8 comments:

AlanSE said...

I'm a little confused by some of your points.

We can all agree that breaking up the trip into smaller delta Vs is good, but that's if you have a propellant source available at those stops. I have the most trouble with this:

"Moreover, given propellant in LEO, an upper stage returning to the earth's surface doesn't have to re-enter at 8 km/s. Given propellant in LEO it can refuel and shed some of it's orbital velocity via reaction mass instead of aerobraking. Eliminating the 8 km/s re-entry makes re-use of upper stages much less difficult."

There's nothing in LEO except for what we take there. Since the propellant will come from some other source, it seems like aerobraking is our only option. The engine reaction velocity won't be much over 4 km/s, which is what it takes to get from EML-1 to LEO. But you won't be getting water directly from EML-1 unless you use asteroids, and those asteroids also have to be moved into EML-1 from somewhere else in the first place... again, using reaction mass.

The moon's water-ice resources are much more certain and abundant. But taking water from the moon to LEO would be a Delta V nightmare. That's 12.6 km/s round trip! Unless you're manufacturing ships on the moon itself, re-usability is the only option here. If you're going to lift water from the surface of the moon to LEO then the ship making that journey would have a terrible mass fraction and the deliveries would barely be a trickle. You'd have to run a huge number of trips to ever get a useful amount of propellant into LEO, which comes from the fact that you need propellant for your ship to make it back from LEO to the moon to make another trip.

If you use aerobraking, then you can make the shuttle between the lunar surface to LEO 9.5 km/s, which is still not very hopeful. But maybe the intent is that an EML-1 station exists, which takes fuel from the lunar surface shuttle and gives fuel to the LEO shuttle. But then it would take lots of trips by the lunar surface ferry for one trip to LEO. Maybe that's your intention. But if you're not using aerobraking, the trip ratio will be huge. How many times can you run the trip from the surface to EML-1 without crashing?

But then again, maybe the idea is that a trip from the lunar surface to EML-1 doesn't wear down the ship, and if the LEO trip doesn't aerobrake, then it doesn't either. Still, a lot of these ratios are going to be very large unless we can use nuclear rockets.

Hollister David said...

Alan, I imagine 3 sets of tankers.

The first set would ferry propellant from the moon to EML1 or EML2. Round trip for these tankers would be 5 km/s

Another set of tankers would move propellant from EML1 or EML2 to LEO. Round trip for these tankers would be 7.6 to 4.5 km/s, depending on how much aerobraking is used to circularize orbit at LEO.

The 3rd set of tankers would ferry propellant from EML to GEO. Round trip delta V for these tankers is 2.6 km/s.

See the delta V map above.

Jon Goff said...

Hop,
I agree on some points and disagree on others. Ultimately, economics matters as much or more than physics on determining what will or should happen. That said, I agree that once you need more than a certain amount of propellant on the Moon, ISRU will likely make more sense. I'm more skeptical about lunar ISRU replacing earth for LEO depots. It *might* happen, but there are a lot of unknowns.

Personally, I think fully reusable launch vehicles for earth are feasible. Which means in my calculus, as demand for propellant in LEO increases, it's an open question on if RLVs from earth will better supply that versus RLVs from the Moon. It's an analyzable problem, but a very involved one that I don't have the time/resources to really dive into right now.

Also, was I misunderstanding your comment about using LEO propellant to reduce entry velocity for terrestrial RLVs? I personally think that's a pretty silly idea. TPS is hard, but not that hard. And you'd have to have a very very low cost of prop in LEO to lower your reentry velocity low enough to really simplify the TPS requirements much.

All said, I'm a big fan of ISRU, depots, and tanker tugs. I'm just not 100% convinced that lunar or asteroidal ISRU will displace earth-launched prop in LEO anytime soon. And by "soon", I mean any time within 10ish yrs of us actually producing our first drop of prop on the moon.

~Jon

Hollister David said...

"TPS is hard but not that hard" Jon, here I disagree.

TPS is quite doable for a capsule. This was demonstrated in way back in the 60's by Apollo. But what's the delta V budget for a capsule? For Dragon to depart from a 400 km altitude orbit and reach an atmosphere grazing perigee takes about .1 km/s. With that sort of delta V budget, more massive structure and TPS is doable.

I think reuse is also possible for a Grasshopper booster stage. The booster doesn't have an 8 km/s budget and doesn't re-enter the earth's atmosphere at orbital velocities.

It is the second stage that I bet against. With an ~8 km/s delta V budget it has to be a cascaron. And the conditions of an 8 km/s re-entry are extreme. If the goal is recovering and re-using a second stage, I believe TPS is that hard and then some.

Hollister David said...

"All said, I'm a big fan of ISRU, depots, and tanker tugs. I'm just not 100% convinced that lunar or asteroidal ISRU will displace earth-launched prop in LEO anytime soon. And by "soon", I mean any time within 10ish yrs of us actually producing our first drop of prop on the moon."

Here we agree. If lunar prop does come to pass i expect it's use to grow in stages. Maybe something like this:
1) Lunar ascent
2) Reusable lunar ascent/landers that move moon's surface and LLO.
3) Reusable lunar ascent/landers that move been moon's surface and EML1/2.
4) Reusable ferries that move between LEO and EML1/2.

I would expect stage 4 to happen decades after prop production started.

jesrad said...

I've been wondering about using EML1 or EML2 as the anchor-point for spatial refueling and assembly. The inherent instability of these Lagrange points make station-keeping a low but constant hassle.

Wouldn't EML4/5 prove more useable somehow ? What about parking in a horseshoe orbit around those points ? The retrograde pass would mean a lesser braking impulse required to go and park there, while the prograde pass could boost any departure from it. And station-keeping would require a lot less fuel over the long haul. Does that sound right ?

But I just have no idea how to calculate those deltaV offsets...

Hollister David said...

Jesrad, I talk about EML1 and 2 vs EML 3 & 4 at my cartoon delta V map.

jesrad said...

Right ! I hadn't realized how easy it is to bump up from EML2 to the interplanetary highway, and was only thinking of Earth vicinity.

Thank you for making this blog, it's a fantastic treasure trove for Kerbal Space Program enthousiasts like me.