SpaceX manned moon landing: Falcon Heavy/Dragon V2

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sevenperforce
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SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby sevenperforce » Mon Jan 04, 2016 10:02 pm UTC

SpaceX has already achieved quite a few firsts: first private company to orbit a liquid-fueled rocket, first private company to launch, orbit, and recover a spacecraft, first private company to complete an ISS mission, and now the first ever return of an orbital-class booster to a powered landing. With the Dragon V2 crew-rated capsule, SpaceX will become the first to recover a fully-reusable orbital capsule using a powered landing (while the Soyuz capsules use disposable retrorockets for final touchdown, they require parachutes first; the Dragon V2 will have backup parachutes but can land on its liquid-fueled SuperDraco engines alone after re-entry).

Ultimately, SpaceX is looking toward Mars missions...but in the nearer future, what might they be able to pull off? Well, there's always the moon. SpaceX already has several option contracts for moon missions.

As it turns out, Falcon 9 v1.2 is already capable of achieving lunar orbit with a 4-tonne payload. So SpaceX could become the first private company to place a satellite in lunar orbit pretty easily. But their option contracts are for landing, not orbiting...and they'd probably want to go for a "first ever" rather than just a "first private ever" accomplishment.

Getting down to the lunar surface is tricky without an atmosphere to allow aerobraking. Falcon 9 v1.2 can't quite manage an actual moon landing: although it has just enough delta-v to reach the surface with about a half-tonne of payload, its single second-stage Merlin 1D vacuum engine can only be downthrottled to 60%, which would be a whopping 11 gees on the craft at that point. Definitely not going to work.

Once Falcon Heavy is operational later this year, though, we have better options. The triple-booster rocket will be able to deliver a whopping 16 tonnes of payload to low lunar orbit. The Dragon V2's SuperDraco engines have a specific impulse of 240 seconds, meaning that a mass ratio of 1.55:1 would be needed to descend propulsively from orbit to the lunar surface. Ordinarily, the Dragon V2 will only carry 1400 kg of propellant compared to its dry mass of 4200 kg and its internal payload of 3310 kg, but that includes about 10 cubic meters of open cockpit volume which would not be used in an unmanned version. The average density of NTO/MMH is about 1 g/cc, so if a retrofitted internal fuel tank was added to occupy just half of that space, it would be enough volume to carry 5 additional tonnes of propellant. Along with the capacity of the internal payload bay, that allows for propulsive landing with a payload of 1255 kg (enough for a small lunar rover). The eight SuperDraco engines can be throttled down to 20% each, and only two are needed for stable thrust (assuming stability corrections from the additional eighteen Draco thrusters), meaning that the minimum thrust is a mild 0.55 gees. That should be well within the limits of a soft landing, allowing Dragon V2 to become the first craft to achieve propulsive landing on two separate worlds.

Seems feasible. Could SpaceX do better, though? Maybe.

The current unpressurized extended trunk on the Dragon family has an internal volume of 24 cubic meters, enough to hold 24,000 kg of fuel. The trunk itself weighs in at around 800 kg. By stacking two such trunks end-to-end underneath a Dragon V2, the total dry mass would go up to 5800 kg with 49,400 kg of fuel. Using a manned Dragon V2 with a crew of 3 rather than 7 would (conservatively) reduce the payload mass cost to around 2000 kg, giving the craft a net mass ratio of 6.3:1, or a total delta-V of 4.68 km/s.

That's enough to make a full descent and ascent between lunar orbit and the lunar surface. The trouble, of course, is getting back from lunar orbit to Earth. I think I know a way they could pull it off, though...

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby ijuin » Tue Jan 05, 2016 8:02 am UTC

To get the return fuel, you would need to put a separate fuel tank in lunar orbit beforehand for the Dragon to rendezvous with.

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby cjameshuff » Tue Jan 05, 2016 12:41 pm UTC

Not that it entirely changes your reasoning, but the Merlin Vacuum has a wider throttle range, down to 360 kN (39%) according to this:
http://www.spacex.com/sites/spacex/file ... ev_2.0.pdf

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby jewish_scientist » Tue Jan 05, 2016 9:23 pm UTC

As I was reading this I stopped every 5 seconds or so and thought, "Man. Spacecrafts have really cool names." Do we know what they plan on doing on the moon? There sure is plenty of options to choose from.
"You are not running off with Cow-Skull Man Dracula Skeletor!"
-Socrates

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby sevenperforce » Tue Jan 05, 2016 10:50 pm UTC

jewish_scientist wrote:As I was reading this I stopped every 5 seconds or so and thought, "Man. Spacecrafts have really cool names." Do we know what they plan on doing on the moon? There sure is plenty of options to choose from.

Well, one option contract is to place a single package of some Japanese soda on the moon as an advertising thing for that Japanese soda company...

...but depending on the payload there are a lot of other options.

cjameshuff wrote:Not that it entirely changes your reasoning, but the Merlin Vacuum has a wider throttle range, down to 360 kN (39%) according to this:
http://www.spacex.com/sites/spacex/file ... ev_2.0.pdf

Oh, interesting! That may prove useful.

Using an earlier launch to put additional fuel reserves in lunar orbit is one possibility. Unfortunately, stacking two extended trunks carrying fifty tonnes of fuel would already put the total launch weight far above the 16-tonne LLO payload capacity of Falcon Heavy. Another problem is the landing itself; trying to land the Dragon with a 24-tonne fuel reserve trunk strapped underneath will be rather unstable.

I think there's an elegant solution. Falcon Heavy's payload is for a low lunar orbit...but what if stable lunar orbit is never the goal?

Rather than flying into LEO, then doing a Hohmann transfer to LLO, then flying down to the lunar surface, we could try something a bit different. A bi-elliptic transfer typically takes more time than a Hohmann transfer but is more efficient in cases where the final target orbit (in this case, the semimajor axis of the Moon's orbit) is 12 times the initial orbit (the surface of the Earth) or more. Rather than jumping from LEO to LLO, let's imagine a trajectory starting from a fictional orbit at Earth's surface.

Falcon Heavy will be equipped with a novel propellant crossfeed mechanism, where all three launch engine clusters draw fuel from the two auxiliary boosters up until initial separation. This allows the central booster to "start fresh" with a full tank after shedding the weight of the two auxiliary boosters, increasing the effective delta-V. In most cases, this is ideal...but not all. Maintaining higher thrust for a greater duration during launch (by feeding all three engine clusters equally) will result in a more rapid acceleration, which is better for certain transfer orbits which need to maximize the Oberth effect. Since a trajectory starting from Earth's surface needs to get out of the atmosphere as quickly as possible, this will be ideal.

So suppose the Falcon Heavy boosts to an elliptical orbit with perigee at 6,378 km and a velocity of 1.08 km/s at a distance of 363,000 km (the moon's perigee), then executes a slingshot with gravitational assist to move it into an orbit just outside the moon's and a slightly higher velocity, so that it will cross the moon's sphere of influence on the return trip with the minimum possible perilunar velocity:

bi-elliptic free injection.png
bi-elliptic free injection.png (4.43 KiB) Viewed 4844 times

The red orbit is the first ellipse; the green hyperbolic slingshot moves the craft into a wider orange orbit that just barely exits the moon's sphere of influence, and then the moon "catches up" to the craft such that it free-falls into a lunar capture with the lowest possible perilunar velocity.

I'll have to do a bit of math to figure out the payload at this point, but it will be much higher than a LEO-LLO trajectory. The upper stage of the Falcon 9 would fire its engines in retrograde with a near-suicide burn to a standstill just above the lunar surface, then the Dragon V2 would detach. The upper stage would resume firing, achieving a low lunar orbit in the opposite direction while the Dragon V2 would descend the remaining 1 km or so with nothing more than gravity drag to fight against. Since lunar gravity drag is so low, this would enable the Dragon to reach the surface by itself without any trunk, but with significant remaining fuel reserves, and with the Falcon upper stage in a low orbit ready to pick it back up for the return trip.

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby ijuin » Wed Jan 06, 2016 1:17 am UTC

Two questions. First of all, can the Dragon launch and dock with the booster stage and then return to Earth from this landing situation?

Second, how much additional time will it take as compared to the classic fail-safe Free Return trajectory used for Apollo? Astronauts are gonna burn up consumables while they wait to get there, after all, and past a certain point the consumables mass more than the propellant saved from a lower delta-v requirement.

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby sevenperforce » Wed Jan 06, 2016 4:28 pm UTC

ijuin wrote:Two questions. First of all, can the Dragon launch and dock with the booster stage and then return to Earth from this landing situation?

The upper stage would most likely be coupled to a Dragon 1 capsule with the shortened version of the fairing connecting it to a Dragon V2. On separation, the fairing is discarded and the Dragon V2 descends to the lunar surface. Upon return, the Dragon V2 launches and mates nose-to-nose with the Dragon 1 capsule (ISS docking ports are androgynous), taking on supplies and fuel for the return trip using the Merlin 1D Vacuum from the upper stage:

Spcxmnndlnrmssn.png

This will allow the Dragon V2 to take on additional supplies and fuel for the return trip, while still remaining the sole manned landing craft. Having a sole manned landing craft is part of the "first" aspect of the whole mission profile. No one has ever come close to fielding a manned spacecraft capable of landing on another world and then returning to land on Earth.

Second, how much additional time will it take as compared to the classic fail-safe Free Return trajectory used for Apollo? Astronauts are gonna burn up consumables while they wait to get there, after all, and past a certain point the consumables mass more than the propellant saved from a lower delta-v requirement.

Probably not very much...the requirements are pretty narrow either way. The delta-V savings come more from using a surface-to-surface profile and less from using an extended bi-elliptic transfer. The Apollo landing missions had to reach LEO, enter a Hohmann transfer and move from the Hohmann orbit to a lunar orbit before the lander could break off and descend. In contrast, the Falcon 9 upper stage would "drop" the Dragon V2 lander before entering lunar orbit.

Having additional supplies tucked away in the Dragon 1 will also help with the consumables issue. Plus, the return trip can be executed more quickly than with Apollo and will require less fuel, since the Dragon V2 is far more flexible and maneuverable as far as re-entry is concerned.

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby sevenperforce » Wed Jan 06, 2016 8:46 pm UTC

Trying to find the ideal lunar approach trajectory...it's a bit tricky.

The grey region in the image below is the Hill Sphere of the moon. Technically, the moon's gravitational influence extends all the way to Earth, but for the purposes of estimating delta-v, we can pretend that the Earth's gravity is switched "off" and the moon's gravity is switched "on" when you cross from the blue region into the grey region (and vice versa). At its perigee, the moon is clipping along at a respectable 1,080 m/s, so this must be subtracted from the velocity vector of the spacecraft when it crosses the line.
Spoiler:
mnhllsphr.png
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In order to do an initial separation at near-zero velocity, we need to find the orbit which, after crossing this boundary, crosses the lunar surface with the lowest possible speed, accounting for the subtraction of the moon's velocity vector. Since specific orbital energy is constant, we find that the speed vf at the lunar surface for any Hill-radius-crossing speed vi can be found as:

vf = sqrt(vi2 + 2μ/RM - 2μ/RH)

Since 2μ/RM - 2μ/RH is constant, it's obvious that vf will reach a minimum when the magnitude of the entry velocity is at its lowest. Since we subtract the velocity of the moon, we find that entry at any point with a velocity vector matching that of the moon results in an effectively zero initial velocity. The entire craft will free-fall to the lunar surface, leaving us with vf = sqrt(2μ*(1/RM - 1/RH)) = sqrt(2*Mmoon*G*(1/RM - 1/RH) = 2.34 km/s.

Spoiler:
mnhllsphr.png
mnhllsphr.png (4.05 KiB) Viewed 4747 times

Now, what is the lowest-specific-orbital-energy Earth orbit which has this velocity vector? Naturally, it's going to be the case where the distance to Earth is lowest...that is, on the near side of the moon's Hill sphere, 305,000 km from the center of the Earth. The semimajor axis of this orbit is 275,000 km. Here's where we'll definitely want to do a bi-elliptic transfer. A typical Hohmann transfer from Earth's surface to any point on this outer orbit would require an initial delta-v of 11 km/s and an apogee burn of 900 m/s:

hohmann 1.png
hohmann 1.png (4.35 KiB) Viewed 4739 times

Gotta do better than that if we're going to have 2.34 km/s for the suicide burn, plus propellant to re-enter a low parking orbit, then pick up the lander, then return home.

Here's where a modified bi-elliptic approach comes in. Using a slightly higher initial delta-v, the spacecraft can cross into the forward (left) side of the moon's Hill radius with a non-zero velocity. When the 1,080 m/s velocity of the moon is added, this becomes a hyperbolic trajectory, slingshotting the spacecraft around the moon and onto a modified but acceptable Earth orbit:

bllptc trns 2.png
bllptc trns 2.png (2.32 KiB) Viewed 4736 times

This will reduce the total launch delta-v to around 11.2 km/s and enable insertion into lunar free-fall without further expenditure of fuel, while only adding a half-day or so to the transit time (due to the initial elliptic transfer being tighter and therefore more rapid).

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby wumpus » Fri Jan 08, 2016 7:42 pm UTC

ijuin wrote:To get the return fuel, you would need to put a separate fuel tank in lunar orbit beforehand for the Dragon to rendezvous with.


More or less true. Judging from historical examples (i.e. I don't think any rocket has discarded a fuel tank (i.e. a non-pendulum fallacy example of what KSPers call "bamboo staging") I would assume that you would put an entire rocket stage in lunar orbit, not just the fuel. But the idea holds. Note that a hybrid rocket (NO2 and "rubberish stuff") would probably be idea in that the fuel wouldn't need cryo-storage (the stuff sits in hot-rodders' engine compartments without significant boiloff issues. I'm guessing it can handle space).

Does anybody know the effects of using an ion-thruster through the Van Allen belts? I thought I heard something about a ESA mission to the moon (2000ish) that would take months due to the ion thruster, but can't find any information. The NASA ion-thruster missions I've read about seemed to have avoided the Van Allen belts altogether and just went straight to escape velocity with chemicals. If you could get the ion-thrusters to take your cargo to the moon, the difference is 40 (or more) mtons vs. 4 (and also all year instead of 3 days. Don't expect LOX much less LH to be around).

I've often thought that after Apollo 11, one of the Apollos should have flown a cargo only flight. Get enough "stuff" for an extended stay. Problems with that:
Not enough automation. Apollo 11 autolander tried to land in a boulder field and Neil Armstrong had to manually pilot the craft.
The plan implies that Apollo 12 would make the most sense to send up as cargo. If 13 went the same is it really did, it would never reach the cargo. There would be even more political problems and more pressure to cancel the program even earlier.

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Re: SpaceX manned moon landing: Falcon Heavy/Dragon V2

Postby cjameshuff » Sun Jan 17, 2016 1:34 pm UTC

wumpus wrote:
ijuin wrote:To get the return fuel, you would need to put a separate fuel tank in lunar orbit beforehand for the Dragon to rendezvous with.


More or less true. Judging from historical examples (i.e. I don't think any rocket has discarded a fuel tank (i.e. a non-pendulum fallacy example of what KSPers call "bamboo staging") I would assume that you would put an entire rocket stage in lunar orbit, not just the fuel. But the idea holds. Note that a hybrid rocket (NO2 and "rubberish stuff") would probably be idea in that the fuel wouldn't need cryo-storage (the stuff sits in hot-rodders' engine compartments without significant boiloff issues. I'm guessing it can handle space).


The Shuttle is the obvious example of a rocket that dropped a fuel tank.
Hybrids have been unimpressive. Virgin Galactic can't even get SS2 to the Karman line, and Sierra Nevada has abandoned the technology for the Dream Chaser's orbital maneuvering engines. Nitrous oxide is N2O, two nitrogen atoms per atom of oxygen, and while relatively storable, it's explosive and not as good an oxidizer as the alternatives. There's storable hypergolics which Dragon already has engines to use, and LOX and methane/RP-1 aren't hard to store for long periods.


wumpus wrote:Does anybody know the effects of using an ion-thruster through the Van Allen belts? I thought I heard something about a ESA mission to the moon (2000ish) that would take months due to the ion thruster, but can't find any information. The NASA ion-thruster missions I've read about seemed to have avoided the Van Allen belts altogether and just went straight to escape velocity with chemicals. If you could get the ion-thrusters to take your cargo to the moon, the difference is 40 (or more) mtons vs. 4 (and also all year instead of 3 days. Don't expect LOX much less LH to be around).


The belts don't make any difference to ion drives, but they do make a difference to the computers of craft traveling through them, especially when those craft are limited to slowly spiraling out through them. Satellites do orbit through them with useful lifetimes though. There's no major problems keeping LOX and methane liquid for the required duration.


wumpus wrote:I've often thought that after Apollo 11, one of the Apollos should have flown a cargo only flight. Get enough "stuff" for an extended stay. Problems with that:
Not enough automation. Apollo 11 autolander tried to land in a boulder field and Neil Armstrong had to manually pilot the craft.
The plan implies that Apollo 12 would make the most sense to send up as cargo. If 13 went the same is it really did, it would never reach the cargo. There would be even more political problems and more pressure to cancel the program even earlier.


The automation issues could be worked around by sending more expendable ground probes capable of scouting out a good landing site and acting as navigational beacons to direct later craft in, but they didn't even get a rover until Apollo 15.


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