Saturday, January 6, 2018

Falcon Heavy Moon Mission Update--Now With Raptor Upper Stage!

I got a comment (I got a comment!!!) from "redneck" on my previous post, which looked at a 2-launch Falcon Heavy architecture for getting crews to low lunar orbit.  He suggested that going for on-orbit refueling of the F9 S2 solved a lot of problems, and I've come to believe that he's right.

While refueling one S2 from another one presents fairly nightmarish plumbing difficulties, reusing one of the second stages from the launch of one of the Falcon Heavies certainly reduces the need to engineer a chopped-down TLI stage and figure out how to launch it within the current FH length constraints. With refueling, you'd launch the Dragon 2 crew module with the lunar maneuvering stage, using the attached FH Stage 2 to do the TLI burn, even though it doesn't yet have enough propellant to meet the delta-v requirement.  Then you'd launch the support D2 on its own, leaving plenty of propellant in its S2 "tanker" stage once it was on-orbit.  After rendezvous and docking the two D2's nose-to-nose, you'd somehow magically transfer the remaining prop from the tanker S2 to the TLI S2, and off you go.

This has many nice properties.  First, you can make the D2's somewhat heavier.  There's still some customization that has to be done for the D2 support module, but it's nowhere near the previous strip-it-to-the-studs requirement we had when we were launching a fully-fueled TLI stage on top of the FH.  I still think that the support D2 probably doesn't have a heat shield and may not have SuperDracos, but my guess is that you can wind up with a lot more common equipment between the two versions.

Also note that our problem with sending the crew D2 ass-backwards into the unknown (and therefore pulling negative gees) has gone away.  That removes the need for couches and control panels in the support D2.

So let's talk about transferring fuel.  The way it's planned for the BFS to do this is to dock tail-to-tail.  That makes a lot of sense if you've designed your stages to do it, but it would require a completely new interstage to do it with an F9 S2, because you have to protect the Merlin vacuum nozzle(s) from damage.

Furthermore, we know we want our D2's docked nose-to-nose.  So we either have to do a whole bunch of undock-turn around-dock to fuel-undock-turn around-redock the payload stuff (which sounds nuts to me), or we have to find a way to transfer fuel from the FH #2 S2, on one extreme end of the docked stack, to FH #1 S2, on the other extreme end.

I can only think of two ways to do this, and both of them will cause the NASA crew safety people to be wearing their brown trousers on rendezvous day:
  1. Extend some kind of double refueling boom (one for the LOX and one for the RP-1) from the the tanker S2, around the LMS and both D2's, to mate with fueling collars on the TLI S2.  You'd have to stow the booms on the outside of the stage, then either swing or extend them, then mate them securely to the collars.  The fact that the two D2's and the LMS exceed the length of the current F9 S2 by almost 7 meters isn't going to help things be any safer or more reliable.
  2. Build refueling lines into the LMS and both D2's to transfer the propellant.  This has actually been envisioned in the IDSS docking standard, but never implemented.  And of course you'd have to figure out how to run the lines through the D2's and their trunks.
This frankly sounds butt-ugly, which is why I didn't consider it in the first go.

However, this isn't our only problem.  After thinking about it some more, I think our stage lifetime problems were more acute even before we decided to try refueling, and now they're even worse.  Here's an arm-wave at just how long it takes before you can do the TLI burn and be rid of all of your S2's:
  1. Launch first FH. (This starts the clock running on the TLI stage life.)
  2. Launch second FH.  Even if you have the ability to launch two FHs into the same launch window (which you probably don't), you have to plan for a glitch on the second one once the first is gone.  That's at least a 24 hour wait for a launch window if you're going to do everything into an inclined LEO (and you are).
  3. Rendezvous and dock the S2+LMS+D2Crew with the S2+D2Support.  The shortest ISS rendezvous has taken about 6 hours.  Let's budget 8.
  4. Do the fuel transfer.  How long this takes depends on the mechanism used, but I wouldn't budget less than 6 hours with checkout, settling burns, transfer, and closeout.
  5. Coast to your TLI insertion point.  Could be as much as 90 minutes.
  6. Throw in 8 hours for things to go wrong, but not quite wrong enough to abort.
Total:  48 hours.

I'm pretty sure that the longest coast from launch to stage restart by the F9 S2 is about 45 minutes, so we're just a tiny bit short.  I am far from an expert in the various design factors that go into increasing stage life, but here are the ones I know about:
  1. Boil-off.  Not a problem for RP-1, but even subcooled LOX will warm up and start to boil, and the boiling will cause it to be vented to avoid pressure buildup.  Boil-off can be minimized with insulation, or by really big tanks.  Since we're pretty much stuck with something close to the F9 S2 form factor, the latter doesn't work.

    Since we only need some of our propellant in each stage reserved for TLI, I wonder if the "header tank" scheme proposed for BFS would work.  Not only does it prevent sloshing during landing (only interesting for the BFS), it also has the effect of putting some prop in a kind of thermos bottle.  If, after achieving orbit, the outside main tank is vented to vacuum, it will insulate the inner tank quite effectively, since it won't be subject to much radiant heating.
  2. Helium.  Everything on the F9 S2 is pressurized with helium, which has its own problems with heating and venting.  Once the pressurant is gone, the stage is dead.  If you could use autogenous pressurization (pressurizing each tank with boil-off from that tank), you could drastically reduce helium requirements and lengthen lifetime.  But you can't do that with RP-1, because its vapor pressure is so low.  (For hopefully obvious reasons, it's a really bad idea to pressurize your RP-1 tank with gaseous oxygen...)
  3. Power.  It's one thing to run all your avionics and actuators off a fairly small battery for less than an hour.  It's quite another to use battery power for two days.  The stage is either going to need its own solar panels, or it's going to have to draw power from the D2's solar arrays through a bus that probably doesn't exist right now.
  4. Attitude control.  If you're using hypergolic or cold gas RCS thrusters, at some point you run out of hypergolics or nitrogen.
I think it might be time to give up on the F9/FH S2.  Is there an alternative?

Oddly, there might be.  We know the US Air Force is interested in developing a Raptor upper stage for the FH.  There are two good reasons for USAF to be interested in this, and there might be a couple that would interest SpaceX:
  1. The second round of Evolved Expendable Launch Vehicle requirements include the ability to put satellite into GEO without attaching payload assist systems.  That requires a longer coast period to get to GTO apogee (about 5.25 hours) before doing the insertion burn into GEO.
  2. In addition to EELV2, there have been rumors that USAF wants to make the X-37C operational.  This is a bigger version of the X-37B, which SpaceX has already launched once.  Rumors are that it's big enough that USAF needs an upper stage with a bit more energy to deploy it for some of its missions.
  3. Beyond just the USAF requirements, SpaceX would have an interest in getting a testbed for some of technologies needed for the BFS, which turn out to be almost exactly the technologies we need up above:  autogenous pressurization (which requires switching from RP-1 to liquid methane), low boil-off of some amount of propellant, and refueling.
  4. In addition, switching the primary second stage for both FH and F9 to the Raptor means that the number of Merlins they have to produce drops to a trickle after they finish building out their fleet of medium-reusable block 5 cores, freeing up line space and personnel to ramp Raptor production.
So, without further ado, let's unveil the new Raptor Upper Stage!  The RUS:
  1. Uses a single Raptor vacuum engine for propulsion.
  2. Uses liquid methane (LCH4) instead of RP-1 for fuel.
  3. Has about 25% more energy than the current F9 S2.
  4. Retains its interstage as a skirt around the engine nozzle, enabling tail-to-tail docking and secure refueling attachments.  Note that the current F9/FH land the interstage as part of the core.  Using it as a skirt for the S2 means that it's no longer reusable.  (This might be a good reason to keep the current F9 S2 in the inventory for lighter launches, although then you're back in the Merlin-making business.)
  5. Has a dry mass of about 7.6 t vs. the ~4 t of the current F9 S2, and a propellant mass of 115.9 t vs. 107.5 t.  (Dry mass is heavier because of  the docking skirt/interstage, and because LCH4 is less dense than RP-1, requiring a bigger tank.)
  6. Is 5 m in diameter, vs. the current 3.66 m F9 S2.  (The fairing is 5 m in diameter, so I don't think this messes up the aerodynamics.  It does significantly complicate the attachment of the D2; My guess is that it'll require a tapered interstage to attach to the existing D2 trunk.
  7. Is slightly shorter than the F9 S2 (due to the wider stage).
  8. Has header tanks inside the main tanks, capable of holding roughly half of the propellant in a low-boil-off state.
  9. Keeps its nitrogen for its cold-gas thrusters in the thermos bottle, and makes the LN2 tanks bigger.
  10. Takes power from an umbilical to whatever is mounted above it.
When I run the numbers on this, everything gets significantly better.  We can now comfortably carry a crew of 5 with a mission duration of 3 weeks.  We can carry at least 1 t of extra (non-crew) payload to LLO.  And we now have one FH launch with two-booster reuse, and one with full reuse.  Here's the mass budget:

Module NameDry MassPayload MassProp MassWet MassEngineSpecific ImpulseDelta-v NeededDelta-v Available
Dragon 2 Crew6,4001,3235008,223Draco300-184
Dragon 2 Support6,4001,3235008,223Draco300-184
Lunar Maneuvering Module1,000-15,30016,300OME (AJ10)3161,9501,950
TLI Stage 27,570-55,72363,293Raptor3753,1903,190
Launch NameDescriptionPayloadLengthLaunch TypeProp at LEO Burnout
FH #1
Tanker + D2Supt
8,2238.12 Booster Reuse41,008
FH #2
TLI + LMS + D2Crew
24,52210.7Full Reuse16,665
Excess Above TLI Delta-v:1,950

The updated mission profile is:
  1. Launch FH #1 as the S2 (RUS) tanker, with the support D2 as payload.  This is a 2-booster-reusable launch.
  2. Launch FH #2 as the S2 (RUS) TLI stage, with the LMS and the D2 crew on top of it.  I'm going to assume that it's better to adapt a 3.66 m LMS to the 5 m RUS and get rid of the interstage than it is to adapt the D2 to a 5 m LMS and keep the interstage through most of the mission.  This flight is fully reusable.
  3. The two launches rendezvous.
  4. D2 support undocks from tanker S2.
  5. Tanker RUS docks tail-to-tail with the TLI stage + LMS + D2 Crew. Propellant is transferred.
  6. Tanker RUS is jettisoned.
  7. D2 support now docks nose-to-nose with the D2 crew.
  8. Now we can do TLI.
Still some unanswered questions:
  1. Obviously the RUS is a lot of work.  If it weren't for the USAF being interested, I'd say it was silly.  But I'm now convinced that you really can't do this mission with the existing RP-1 S2, because you'll never get the stage life you need.  So it's the RUS or nothing.  Given that, taking the lunar requirements into account seems like a pretty good idea. (I'm sure Elon is hanging on my every word...)
  2. Going to a 5 m diameter RUS is a big pain, and interstage weirdness will ensue.  In theory, you could do this with a 3.66 m RUS, but it's a really long, thin rocket when you do.  Seems like SpaceX must be mighty close to the aspect ratio limit already.
  3. Crew safety issues abound here, but you pretty much have to transfer prop at some point.  I suppose that the NASA folks might decide that it would be safer to launch the crew on a third F9, dock with the D2 crew after refueling, transfer crew, undock, and then dock the D2 support, but that requires even longer stage life, and it's actually more docking operations with the crew exposed to the point of contact than the way I have it above.
All-in-all, though, this seems quite a bit cleaner.

If I were really ambitious, I'd spec out a nice lunar lander for this architecture.  I'd guess you'd mount it on top of the LMS, and fly the tanker up with no payload (other than its own prop, of course).

Maybe next time.

Tuesday, December 26, 2017

All I Want For Christmas Is a Falcon Heavy Moon Mission

Trump's first space policy directive makes it official that NASA should go to the Moon first, instead of Mars.  Of course, what it really does is continue to pay lip service to the giant pork barrel that is the Space Launch System and the Orion Multi-Purpose Crew Vehicle.

NASA is still slogging away on the planning for the Deep Space Gateway, which is... closer to the Moon than the Earth, but really doesn't do much about getting to the lunar surface, to say nothing of doing something on the lunar surface once we get there.

A big chunk of the problem here is that Orion simply isn't suited for anything other than being a transfer vehicle where you can spend a couple of weeks beyond Earth orbit without dying.  Even if you get use SLS to launch it to trans-lunar injection (TLI), it doesn't have enough delta-v to insert into low lunar orbit (TEI) and then make it back to trans-earth injection (TEI).  It can just barely make it into one of the non-Keplerian lunar orbits like a distant retrograde orbit or a near-rectilinear halo orbit.  Not surprisingly, those are the main candidates for where to put the DSG.

So, to sum up:  the SLS/Orion gravy train continues.  We've currently spent $11.9B on SLS, with another $7.2B expected through 2021.  Orion has consumed $12.5B through 2016, with another $4.5B expected through 2021.  By 2021, we can expect to have flown two crewed missions, one a lunar flyby, and one delivering the first chunk of the DSG (the power and propulsion element) to lunar orbit.

Two crewed missions.  For $36 billion.

It doesn't matter whether the "goal" is the Moon or Mars, because the "goal" is a fantasy.  SLS and Orion suck up every bit of the human spaceflight effort that isn't devoted to the international space station, so there's nothing for landers, or habitation, or lunar resource utilization.

So, is all lost?  For NASA, maybe.  For the private folks, maybe not.

We have three possible private undertakings that could at least replace the SLS, and one (well, maybe one-and-a-half) that could take over from Orion:
  • SpaceX is about to launch Falcon Heavy.
  • SpaceX is also designing the Big Fucking Rocket and Big Fucking Spaceship (BFR/BFS).
  • Blue Origin is working on New Glenn, and then New Armstrong.
  • SpaceX has the Dragon 2 crewed spacecraft for use in Low Earth Orbit (LEO), which might be pressed into service for deep space with a few modifications.
If the BFR/BFS system works, it's a slam-dunk replacement for everything.  Many analyses of this have been done elsewhere, and it's generally awesome, but we really don't have a clue how feasible it is yet.  Given SpaceX's track record, it'll probably work fine, but it'll be 5 years late.  That would put it into service in 2027.

Blue Origin's schedule is somewhat behind SpaceX's, especially for New Armstrong, and their crewed spacecraft efforts so far have been concentrated on the sub-orbital New Shepherd.  My guess is that BO is unlikely to have a lunar-capable system much before 2027, either.

As it stands, neither of these systems is likely to halt the juggernaut that is SLS/Orion, which will so discredit the NASA human exploration program that it probably won't recover.

So what I'd like to do is explore what can be done with Falcon Heavy.

FH is not a heavy enough system to get to the Moon in one go.  SpaceX claims it'll be able to put 63.8 tonnes into low-earth orbit if all 3 cores are expended, but by my model only puts about 18 t into TLI.  That 18 t would have to carry enough propellant to get into low lunar orbit (LLO), let the crew do whatever they're going to do, and then do a TEI burn to get back to Earth.  For comparison, Orion is about 26 t, and even it can't to LLO and back.

So we're going to have to do multiple launches, and rendezvous with stuff in LEO and LLO.  Let's first get a crew to LLO.

Here's a sample mission to put a crew in LLO, using two Falcon Heavy launches.  I'm going to try to do as much as possible of this with existing SpaceX spacecraft and stages, because modifying space hardware is difficult, time-consuming, and expensive, as well as not being what SpaceX wants to do next.  Given that, this is a long shot, but an interesting long shot that could be useful in some circumstances.

There are four modules associated with this mission:

  1. A fairly standard Dragon 2, with a crew of 3.  Payload for this D2 may be a little lighter than for a normal D2.
  2. A second "support" D2.  This is a standard D2 frame, but the guts have been reconfigured to allow it to act as extra living space, provide extra power, deep space communications, modest environmental control and life support systems (ECLSS) capacity, and various pieces of equipment that are required for longer-duration flights.  (A toilet is an important thing here.)  At the same time, some things aren't required:  a heat shield, the SuperDraco engines, some of the ECLSS equipment (to the extent that the D2 Crew has some as well), etc.
  3. A "TLI stage".  The current Falcon Heavy doesn't have enough oomph to launch something, then push it and something that it rendezvoused with into trans-lunar injection.  One possibility here would be to refuel the FH second stage, but refueling technology with liquid oxygen is tricky and hard to develop.  (This is something that is being developed for BFR/BFS, but is unlikely to be developed for FH.)  So, instead, I've assumed that we can launch a chopped-down version of the existing FH S2 as a payload of the FH itself.  Usually, making shorter propellant tanks isn't a huge modification to an existing vehicle.  However, there are some other challenges associated with this.
  4. A "lunar maneuvering stage" (LMS).  Once you're in the lunar transfer orbit, cryogenic propellants like LOX become very difficult to use, because they boil off after more than a few hours.  Since it takes 3 days to get to lunar orbit, execute the LOI burn to enter LLO, do the mission for a few days, and then do the TEI burn to get back to an earth transfer orbit to go home, these two maneuvers need to be done with "storable" propellants, usually a hydrazine fuel and a nitrogen tetroxide oxidizer.  SpaceX has two low- to moderate-thrust engines, the Draco and SuperDraco, that use these propellants, but they're not quite efficient enough to do the trick.  For that reason I've assumed that the LMS is based on a space shuttle Orbital Maneuvering Engine, which is itself a variety of the same engine used for this purpose on Apollo and the Space Shuttle, the AJ10.
The trick is to figure out the mass and delta-v budgets for all of these.  Here's what I got:

Module NameDry MassPayload MassPropellant MassWet MassEngineSpecific ImpulseDelta-v NeededDelta-v AvailableLaunch
Dragon 2 Crew6,4008831,0008,283Draco300-430FH #1
Dragon 2 Support4,2002,6485007,348Draco300-207FH #2
LMS1,000-14,58515,585AJ103161,9501,950FH #1
TLI Stage3,000-52,97055,970Merlin 1D3483,1903,190FH #2
FH #123,86711.2
FH #263,31814.4

The payload masses (i.e. the amount of mass needed for humans and consumables, along with mass above and beyond the D2 base mass aren't quite SWAGs, but they're close.  Note also that I'm guessing that more than 2 tonnes can be gutted from the support D2, when we remove heat shields, SuperDraco thrusters we don't need, parachutes, etc.

Note that the order of these is a bit odd.  The idea here is that the things at the bottom of list push all the things at the top.  So any change to the LMS or D2 masses will make the TLI stage need more propellant to meet its delta-v budget, which will likely make it too heavy to launch with anything else.

The delta-v budget (i.e., the change in velocity each module must produce to fulfill its mission), is ultimately what controls the size of the TLI and LMS systems.  More delta-v takes more propellant, which requires more propellant to accelerate the extra mass, which makes everything still more massive, which requires more propellant, and so on.  Rocket delta-v is determined by the ratio of the "wet mass" (the mass with propellant) to the "dry mass" (the mass when all the propellant for a particular stage has been expended), and the exit velocity of the rocket exhaust, which is the "specific impulse" (oddly measured in seconds, for mostly historical reasons) times Earth's gravitational acceleration.  For the math geeks:

Δv = 9.8Ispln(Mwet/Mdry)

Note:  "ln" is the natural logarithm function, and the "Mwet/Mdry" term is called the "mass ratio". The natural log falls off quite sharply as you reduce the mass ratio close to 1 (which would mean that you had no propellant), so keeping the payload and parts of the spacecraft that aren't propellant as light as possible is incredibly important, as it keeping the propellant mass of stages further up the stack (which just looks like payload to the currently thrusting stage).

Here's what the mission profile looks like:
  1. FH launch #1 takes the D2 Crew, mounted on top of the LMS, to LEO, where the crew waits for the second launch.  Note that the total payload is a little less than 24 tonnes, which is easy for an FH.  I'd expect that the FH's 2 boosters and 1 core can all be recovered and reused from this launch.
  2. FH launch #2 takes the D2 Support, mounted on top of the TLI stage, to LEO.  This mass is a bit more than 63 tonnes, which is right on the hairy edge of what an expendable FH can take to orbit.  This is a very near thing, and even small changes in the payload or structural mass of the two D2's will probably blow the budget and require a third launch.  For various practical reasons which will be explained, this would be a big problem.  One would also think that this should be launched first, since there's no point in risking the crew if the TLI/D2 Support launch fails.  Again, there's a reason for this.
  3. The TLI Stage/D2 Support and the LMS/D2 Crew rendezvous with each other.  The two D2's are equipped with docking adapters, and dock nose-to-nose.  When this is done, the LMS is (facing backward) at the "front" of the 4-module system, followed by the D2 Crew (also facing backward), the D2 Support (facing forward), and finally, the TLI stage at the back.
  4. Since the D2 Crew module is currently facing backward, the crew has to transfer to the D2 Support module before the TLI burn.  Otherwise, they'd have a significant acceleration trying to pull them out of their seats.
  5. The TLI stage fires to insert the stack into a lunar transfer orbit.  This requires about 3190 meters per second of delta-v.  Once the TLI burn is complete, the TLI module is jettisoned.
  6. On the way to the Moon, the crew uses both D2 modules as their living space, as they do while they're in LLO.
  7. When it's time to enter LLO, the three remaining modules slow down by using the LMS to do the Lunar Orbit Insertion burn.  LOI takes about 940 m/s of delta-v.
  8. Now that the crew is in LLO, they perform their mission.  Presumably, this will involve rendezvousing with some pre-positioned chunk of hardware to do stuff, since everything we're talked about so far is  only there to get them to and from LLO, not do anything there.  How you launch that hardware is an exercise left for another day.
  9. When it's time to come home, the LMS does a second burn (the "TEI burn") to inject the spacecraft into an Earth transfer orbit.  This requires about 1010 m/s of delta-v.  After this is complete, the LMS is discarded.
  10. The only thing left now are the two D2's, mated nose to nose.  As they approach Earth, the crew climbs into the D2 Crew, seals the hatches, and discards the D2 Support module.  It'll either burn up in Earth's atmosphere because it doesn't have a heat shield, or a small maneuver from its thrusters can launch it out into deep space so it doesn't clutter up Earth orbit.
  11. The D2 Crew jettisons the Dragon 2 trunk (which has most of the solar panels on it), then turns to reenter Earth's atmosphere.  Note that, just like Apollo, it doesn't try to enter Earth orbit.  That takes too much delta-v.  So it just barrels straight into the atmosphere, using it to slow down.  (The D2 heat shield was designed for this in mind.)
  12. The D2 Crew lands, probably using parachutes.
This whole sequence has been designed to use as much existing SpaceX hardware as possible.  But, since there are always mission-specific tasks required of any space systems design, some things are not perfect.  Here's the list of the things that are the biggest issues.
  1. First and foremost is a little oddity called "dwell time" or "maximum mission duration", and it applies to the TLI stage.  Simply put, it's the amount of time the stage can live in space and still fire its engine.  The FH S2 uses kerosene and liquid oxygen as propellant.  While the kerosene isn't much of an issue, the LOX literally boils as it warms up.  This, along with how long you can maintain power to the stage (it has no solar panels, only batteries), and how long you can keep enough gaseous helium to pressurize the stage, means that all the burns the stage needs to do need to be done quickly.  That's why we launch the FH with the TLI second.

    Even so, it takes a while to rendezvous, dock with the other stack, do checkout, and line up for the TLI burn.  Right now, the longest the FH S2 (which is identical to the second stage on the Falcon 9, BTW) can manage is about 45 minutes.  My guess is that that needs to be at least 4 earth orbits, or about 6 hours.  That's a hefty design change.

    To do that, changes need to be made to better insulate the LOX tanks (which in turn keeps the helium tanks, which are inside the LOX tanks, cold) and either to add more batteries to the stage (which is heavy), or to get it to deploy temporary solar panels for power. Remember also that the TLI stage is shorter than the FH S2, which also requires testing. All-in-all, it's a fair amount of work, even though we know that the Merlin 1D engine is well tested and capable of doing on-orbit restarts.

    An obvious question here is why we don't just use storable propellants, as we do in the LMS. The answer has to do with specific impulse. Storable propellants don't have the necessary exhaust velocity to keep the TLI stage at a size that's capable of being launched with the D2 Support module on an FH. However, if we decide we want to put everything together in 3 launches instead of two, a storable TLI stage might be a better option. However, rendezvousing three separate spacecraft is something that we have no experience doing.
  2. The other problem with the LOX on the TLI stage is that it involves filling the stage just before launch. Since the FH would consider this stage "payload", there are no on-pad facilities to do this. They'd need to be added. That's time-consuming and expensive.
  3. SpaceX doesn't have any piece of hardware that's comparable to the LMS.  It has engines, the Draco and SuperDraco, that use storable propellants, but the SuperDraco is designed more for thrust than specific impulse, and the Draco is more of an attitude control thruster and doesn't have enough thrust.  In any case, it would require developing an entirely new stage.

    That's not the end of the world. The AJ10 is just about the best-understood engine in existence, and it's been used for many different applications, from the Apollo service module to the Space Shuttle Orbital Maneuvering System. Still, a stage is a stage, and it comes with a minimum amount of design and test effort to make it flight-ready. Considering that we'd be launching it with the D2 Crew module (which contains, you know, crew), getting it flight-rated is especially onerous.
  4. As I mentioned above, while the D2 Crew is (or will be) pretty much off-the-shelf, the D2 Support is going to be gutted to the studs and filled up with new stuff.  The D2 Crew doesn't have enough environmental support, power, or deep space communications to be used beyond Earth orbit as-is.  All of that stuff needs to got into the D2 Support.  Again, it's non-trivial work.  That said, working with a flight-proven spacecraft design is a huge step forward.  But mixing and matching equipment and payloads for both D2's so that we stay within our mass budget is tricky.
  5. While docking in LEO is well-understood, docking two pairs of modules would be a little hair-raising.  Long thing things have a high moment of inertia, which requires a hefty thruster system to control.  This further complicates the construction of the TLI stage and the LMS, and increases the possibility of a failed docking.
  6. Note that, at one point, the TLI module is firing while the D2 Crew module is backwards.  As it turns out, because the Merlin 1D wasn't designed for this type of orbital maneuvering, it actually has more thrust than we'd like.  By my calculations, gee forces between 1.2 and 1.8 g would be trying to pull the crew out of their seats, even if the Merlin was throttled down to minimum thrust.  Not only does this require having crew couches and controls in the D2 Support (which adds mass), but it also means that the D2 Crew module needs to be qualified to be accelerated ass-backward into the unknown.  Since this has probably never been tested, it probably doesn't work without some effort.
  7. There are currently no plans to use the FH as a crew-capable vehicle.  All D2 launches are currently planned only for the Falcon 9.  NASA is incredibly risk-averse, and launching a D2 Crew on an FH would require months of certification work.  Add on to that the fact that it would launch on top of the LMS and rendezvous with a stage filled with LOX and kerosene, and you'll have quite a time convincing NASA that this is adequately safe.
  8. While D2 spacecraft are considerably shorter than the fairings used for launching satellites on the F9 and FH, the combinations of the D2 and the TLI stage or LMS are somewhat longer than the usual fairing.  That requires a careful reexamination of the structural and aerodynamic loads that the new spacecraft would put on the launch vehicle.
  9. The current D2 solar panels are attached flat to the trunk.  Whether this will generate enough power to enable crew operations in lunar orbit is an unknown.  If more solar panels are needed, they'll have to be deployed after the TLI burn, which would put too much structural stress the solar panel mounts.  That's a bit of a no-no from a mission safety standpoint, because you don't want mission-critical stuff done after the checkout in LEO, in case you need to abort.
  10. And of course we haven't talked at all about why you'd send crews to LLO in the first place.  Just as the SLS/Orion/DSG is a system with no mission, there would also have to be a lunar lander system, launched on at least one, and probably more, FHes, or some other launch vehicle.  That's still more design work, more fabrication of new hardware, more testing, and more crewed certification.
Would SpaceX want to do this work?  Almost certainly not without major encouragement from NASA.  But if they get antsy about not having a presence on the Moon before the late 2020's (if, for example, the Chinese made a push to have a presence), counting on the SLS/Orion system is economic folly, and counting on the BFR/BFS or New Armstrong might be political folly.  In that case, cobbling together a system mostly out of SpaceX's leftovers might be the least of all evils.

The other possibility is that SLS/Orion suddenly falls out of favor.  It's increasingly more difficult to justify these programs as anything other than pork, with some of its erstwhile patrons getting more and more nervous about appearing to be stupid in public.  If the dam finally bursts, a lot of money would be freed up for NASA to develop real live spacecraft.  If NASA were to get out of the launcher business and wish to remain in the space hardware business (which they should--on both counts), FH would be an awfully attractive way to get started.  I doubt very much that NASA will wish to cede the entire spacecraft business to SpaceX and the BFS.  Given that, using the FH creatively might be pretty attractive.

Sunday, September 11, 2016

In Which I Go Full Tinfoil Hat on the SpaceX Explosion

The SpaceX explosion last week was a big bummer.  But it turns out that it's merely the leading edge of The Alien Invasion.

Well, probably not.  But something very weird is going on.  Here's a GIF I built (lovingly from screen shots) of the video that everybody's now seen:

See the little speck coming in from the right?  If you go to the video (watch it in HD to do this right) and step through at full screen (which it turns out you can do in YouTube by pausing, then hitting '.' to go forward and ',' to go back--who knew?), it looks like a bird.  It even kinda flaps.  But there's something strange about this "bird":

It's moving at about mach 1.

Now, if you watch the video, there are all kinds of birds and bugs flying around between the camera and the rocket.  And of course, the closer those critters are to the camera, the faster their apparent angular velocity, so we shouldn't get too worried about them.

Except this "bird" seems to go behind the northeast lightning tower.  That means that it's actually behind the vehicle, about 2.7 miles away, not gamboling carefree a few yards in front of the camera.  There's exactly one frame where the "bird" is in the line-of-sight of one of the towers.  It's one of the last frames in the GIF, in the leftmost tower.  Here's a blowup of it:

This isn't quite definitive, but it sure looks like it's behind to me.  So let's run with it:

The slowest that an object in the field of view can be going is when it's moving perpendicularly to the line of sight.  To work that out, I used Google Maps/Earth to match the view of SLC-40 we see in the video.  That gives us a rough bearing:  west-southwest.

To get it more accurate, we can time the gap between when we see the first explosion on the video and when we hear it on the audio.  It comes out to 12.5 seconds.  Assuming that it was 80° F at test time (the high was 88 the low was 74, and it was a morning test), the speed of sound would have been 1139 ft/sec.  That makes the distance from the vehicle to the camera (or at least to the microphone) about 2.7 miles.

Turns out that there's yard with a bunch of junk in it 2.7 miles away from the pad to the WSW.  Here it is:

So now we have a pretty good bearing.

Note that, in the GIF, the flying object is right over a hemispherical pressure tank to the right of the image, and it takes exactly 12 video frames, each @ 33.3 ms, to get to the point where it's behind the tower.  That's almost exactly 400 ms of time.

If you draw a line that's perpendicular to the line of sight behind these two objects, you get a distance of about 470 feet:

470 ft in 400 ms gives you a speed of 1175 ft/sec.  Remember the speed of sound was 1139 ft/sec?  That "bird" is moving at just a tad over mach 1.

Birds don't do that.

This is all nuts, obviously.  Even if the... I guess we'd better call it the "flying object", and at this point we can't exactly call it identified...  really is moving at mach 1, it never touches the vehicle, so it would have to:
  1. Somehow release something to bomb the rocket.  This is probably at the hairy edge of possible with technology that's sorta-kinda almost there.  You could probably trash the thing pretty well with a decent-sized ball bearing at that speed.  Or...
  2. Use some kind of death ray as it flew past.  But this simply doesn't exist in a bird-sized form factor.  I'm not sayin' it's aliens (but it's aliens...).
Massive holes in both of these:  First, when you drop things, they can't suddenly leap ahead of you, so our ball bearing has to have some form of propulsion.  (Aliens!!!!)  And second, why would you go to all this trouble when it would be easier to plant somebody in the scrub a mile or so away with a .50 caliber sniper rifle?  (Unless they were aliens...)  And of course there ain't no stinkin' death rays (except the ones created by aliens...).

Finally, if we've got a trans-sonic UFO, where's the sonic boom?  Well, there might be an answer to that one.  If you listen to the video with headphones, starting at about 1:15, we can hear the following events (the ranges are frame numbers from that spot):

000-000 Distant thump, left channel
030-030 Distant thump, right channel
044-050 Metal-on-metal squeal
096-103 Metallic clank
125-125 Click
174-175 Hiss from some sort of pressure release
251-251 First explosion heard

Remember, this is all happening 2.7 miles away on a humid Florida morning, which means that any high end sound will have gone bye-bye long before it reaches the mic.  So the metal-on-metal squeal, the clank, the click, and the hiss are probably from some source much nearer to the mic.  But the distant thumps sound an awful lot like sonic booms.  Unfortunately, you'd expect to hear them first to the right, then the left, instead of the way they are on the video.  But it's not inconceivable that somebody plugged their boom mic in backwards and didn't notice.  That would give a pretty reasonable accounting of the object from a sonic perspective.

And, since the tinfoil hat fits very snugly this evening, two more things:
  1. If you watch the "bird's" "wing" two frames after the explosion, it's illuminated by the flash.  That's a lot more likely to happen if the wing is behind the vehicle and reflecting it back toward the camera.  (On the other hand, if it's a bug instead of a bird and very close, light might shine through a transparent wing.  Doesn't look like a bug, though.)
  2. What's Elon Musk doing asking for photos and videos from the public?  They've got that pad blanketed with high-speed cameras.  It doesn't make sense unless SpaceX thinks that the cause might be external to the pad (or maybe external to this world...).
That's all I've got.  If it turns out that there's some artifact that makes the bird/bug/UFO actually in front of the tower, then we're done.  But the evidence for it being behind the tower is pretty compelling.

So yeah:  It's aliens.  They want to scuttle our space program, and nobody told them, "Klaatu berada nikto".

Update, in the cold light of day:  It's a bug. It's a particularly determined and disciplined bug that flies in an almost-straight line, but it's a bug nonetheless.  It has legs hanging down.  It has transparent wings, visible in more than one frame.  It doesn't quite fly in a straight line, or at the same speed.

As for it going behind the tower, it looks like it's an artifact of the video encoding.  During the early phases of the explosion, another bug, moving lower left to upper right, crosses the southwest tower after being obviously in front of the explosion (you can see it silhouetted against the fireball), and it shows the same sort of artifact, where the encoder prioritizes the in-focus static structure and simply refuses to render the moving stuff in front of it:

Oh, one other thing:  The GIF was made from a 1080p60 video, so each frame is only 16.67 ms.  So the object would moving at mach 2, not mach 1.

And it did occur to me that one of the reasons that Elon would want other media is because if you want to prove conclusively that it's a bug, all you need is a shot from any other angle--which won't have the bug--and you're done.

So:  not aliens.  But of course that's exactly what they want us to think...

Yet Another Update, 9/18/16:  I've clearly been retired from the MPEG business for too long, because there's an obvious explanation for the video artifact.

MPEG (aka H.264) encodes three different kinds of video frames.  I-frames occur periodically and encode the entire picture, but in between I-frames (which have to be very large), are P- and B-frames, which encode changes from the picture in the I-frame (P-frames encode changes after an I-frame, and B-frames encode changes that occurred before the next I-frame.)

If you've got a bug flying in front of the tower, the tower is obviously not moving, so the pixels covering the tower (which are encoded in a 16x16 pixel square called a macroblock), would only be encoded in a subsequent P-frame if something substantially different covered up part of the picture.

Encoders are all a little bit different, but a huge amount of engineering time and effort has been spent on deciding when the human eye would detect that something about the picture has changed, and then only generating the relevant macroblocks in the P-frame if that threshold was exceeded.  Since the part of the bug that covered up the tower is pretty much the same color and greyscale as the tower itself, the encoder simply didn't generate the macroblock.  On the other hand, the part of the bug that's silhouetted against the sky is an obvious change, so the encoder updated that macroblock.

Result:  only the part of the bug against the sky was encoded, making it look like the rest of the object is behind the tower.

Tinfoil hat completely removed and tossed in the garbage.

Friday, May 27, 2016

The Decline and Fall of the Low-Skill Labor Market

I've finally gotten around to drawing some diagrams that help explain why the bottom half of the income distribution in the US is (quite rightly) so fearful, angry, and... well, Trumpy.

For convenience, I'm going to divide the job market into low-skill (you can get the job and work immediately if you have a couple of years of high school), medium skill (you don't need book smarts, but you do need to be trained or at least practice your trade to get good at it), and professional (you need extensive training and theory before even being hired, and then you need substantial experience on the job to get good at it).

Here's a chart of the three labor markets, ca. 1980, and how they got their labor, and how that labor eventually flowed up and out of them:

In 1980, all three of these segments functioned well, because there were numerous pathways between the low- and medium skill markets.  High school kids or low-skill immigrants would start with a job that would give them the work habits they needed either to get promoted into a medium-skill position or to find a medium-skill job based on their resume.  Because the low-skill market was a stepping stone, it had high turnover, supply matched demand pretty well, and wages were stable.

Only people with a reasonable chance of completing higher education went to college.  The best of them got professional jobs.  Those that finished or almost finished could expect that their major mattered a lot less than the credential, and could expect to be ushered into at least a decent medium-skill job.

By the oh-oh's (I'm still flogging that one over the "aughts"--it seems to capture the basic mood considerably better), some bad things were starting to happen to the low-skill labor market, and they're really kicking in right now:

The root of all of these problems is that automation kicked in first in the medium-skill jobs.  All of those knowledge and clerical jobs got their productivity boosted enormously be automation.  They may not have been done completely by a robot, but some hunk of software allowed the job that used to be done by ten people to be done by one or two.  The other eight or nine joined the ranks of what I think of as the "previously skilled":  they're people who have good work habits and demonstrable ability to learn a medium skill job, but there simply aren't enough medium skill jobs to go around.

Some of them got repurposed into organic job growth, or into new niches that opened up as businesses changed.  That's just the old "creative destruction" dynamic and, while it's uncomfortable for the displaced worker, it's not a disaster.
What is a disaster is that when the medium-skill labor market isn't growing very well, there's no need to go fishing for new recruits from the low-skill market; the ones you have will do just fine.  So suddenly, the best that the high school grads, the low-skill immigrants, and the previously skilled can hope for is to hang onto the low skill job that they landed.  Mobility up into medium-skill positions dries up.

The dearth of medium-skill jobs has had another effect:  All of those college kids that graduated with a philosophy degree or a BA in English Literature?  There are people floating around in the medium skill pool who have better qualifications for the remaining jobs than they do.  What growth there is in that market can be filled by explicitly hunting for grads who are trained in the fields that they need.  No need to pay any attention to those "well-rounded" applicants.  So even workers who graduated find themselves playing Chutes 'n' Ladders into the low-skill pool, with no way out.  Maybe we should call these people the "inappropriately skilled".

But it gets worse still.  Not only have we clogged the outlet from the low-skill pool but we've also added in new sources of bodies, in the form of the previously- and inappropriately-skilled.  So we have the supply of low-skill labor exploding and, while demand in the market is growing at a pretty normal rate, it can't possibly keep up with the supply.  That means that that low-skill wages are going down.

Note that the upper end of the job market--the professional jobs and the medium-skill ones that consume experienced workers or appropriately educated grads--are still working just fine.  But the low-skill pool is in terrible distress.  Those jobs don't provide a living wage and they are now truly dead-end jobs.

The only way out is through some sort of retraining, but retraining is expensive.  And how do you support yourself while you're in school?  Even worse, the odds of a retraining program actually helping you aren't great.  If you're coming from the high school track, you may not have the study skills necessary to learn something new.  Humans start to lose their plasticity in their twenties, so suddenly becoming a good student if you weren't one already is not a very good bet.  And even if you are retrained, the medium-skill pool is still in flux; there's no guarantee that the job you're training for won't be automated by the time you're competent to perform it.

If you're in a dead-end job that doesn't pay a living wage, social problems start to set in.  You start losing jobs, because they're all equally dismal and all equally non-remunerative.  You go through periods of unemployment, which makes it even less likely that you'll climb back into the medium-skill stuff.  Eventually, you may drop out of the labor market entirely.

So what happens from here?  I'd like to say that things get better, but I doubt it:

The next big, big thing to hit the beleaguered low-skill market is that, just as automation stunted demand in the medium-skill sector, it will soon do so in the low-skill market.  Add in self-driving trucks, robo-burger-flippers, and the odd construction bot, and suddenly we have the same dynamic of driving people out of the market with no way to get back in.  But now there's no place to go.  The chute drops you into unemployment, with no ladder back out.  Eventually, you become discouraged and drop out of the labor force.

Note also that the job market for new high school graduates becomes wildly untenable.  They may bull their way into the few remaining low-skill jobs, but the "unemployed" bin will always beckon.  Some of them may not even make it into the labor force at all, graduating directly into long-term unemployment.

About the only bright spot in the picture is that the education system will eventually adjust.  It's likely that it will have better success choosing qualified applicants (and the applicants will have better success in choosing a sustainable career), and better pedagogy can make the educational experience more successful.  But none of these trends is likely to halt the relentless attack of the robots.  Unless you possess extraordinary skills, you're in for a very uncertain future--one where downward mobility is unlikely to be just a temporary setback, but instead a sharp ratcheting down of one's standard of living, with little hope of recovering it.

There are four policy implications for this, three medium-sized ones and one huge one:
  1. Minimum wage laws are counterproductive, because they encourage automation.  Even local minimum wage laws can be devastating, because it only takes one incentive to invent the robo-burger-flipper once in LA or Seattle to poison the entire labor pool with the innovation.  Forgoing minimum wage increases won't stop the progression of automation, but at least it can avoid accelerating it.
  2. I've avoided talking about immigration above, but it's pretty clear that you need to consider low-skill immigration separately from medium- and high-skill immigration.  Yes, everybody's annoyed that evil employers are cheating on H-1B visas, but most of those are rolling into stuff that straddles the line between medium-skill and professional.  Those immigrants may displace domestic labor, but they're unlikely to send the displaced down the chute.  On the other hand, low-skill immigration is yet another inlet into the low-skill labor pool.  It's not even close to being most serious of them, but it sure doesn't help.  I can't really justify an immigration policy that makes things even worse for the most economically vulnerable natives.  At the very least, we ought to take a breather on the low-skill immigration.
  3. I also haven't talked about offshoring and outsourcing above.  That's because those are really just variations on the automation theme.  It's true that we're displacing medium-skill labor with cheap overseas labor, but that labor would be useless without numerically controlled drill presses and just-in-time logistics and remote management.  If you were suddenly to repatriate all of those offshore, previously medium-skill jobs, you'd discover that they'd all fallen into the low-skill category--which is why they were able to go offshore in the first place.  Ending offshoring (or free trade, or whatever hideous Trumpian nightmare is being proposed this week) is a lot like goosing the minimum wage:  If anything, it will hasten the end, rather than making things better.
  4. And now for the big one:  That circle in the upper right-hand corner of all three charts, the one that says "retired or out of labor force"?  That's just a giant entitlement sink, soaking up every possible federal and state dollar that can be scrounged--usually from things that are essential governmental functions.  We're going to need to figure out how to build a functional welfare state, or we're going to have to learn to live with a lot of our fellow citizens leading third-world existences--complete with third-world violence and the occasional armed insurrection.
That welfare state, or the lack thereof, is the thing that puts us in the direst peril.  We're almost certainly going to have to raise taxes on the functional parts of the economy, at least a little, but even more important is that we're going to have to reform the system so that we acknowledge that a whole bunch of people can't just be coerced into working if only we squeeze them hard enough.

When you actually look at how the money is doled out today, a lot of it goes to things that aren't particularly helpful in keeping one's head above water if one is unemployable.  We're spending a lot of money on Pell grants for inappropriate education (see above).  We're sending social security old-age benefits and Medicare to some people who don't need them--or at least who don't need them as much as somebody with no income or wealth at all.  And, maybe the biggest sink of all, we're spending huge sums on Medicaid, which may provide mediocre health care for poor people, but it can't keep them housed, clothed, and fed.  Somebody needs to take a long, hard look at Maslow's hierarchy and do some very unpleasant things.

Saturday, February 6, 2016

Security for Wind and Solar Energy

I've slowly become convinced that an electric power grid that was predominantly wind and solar might actually work and be cost-competitive.  It obviously depends on a big maturation of energy storage technology, but that seems to be moving forward.  As long as it scales as fast as fossil plants or nukes, and is as cheap, reliable, and dispatchable, wind and solar can fill the bill.

But in addition to those usual metrics for the power market, there's another that we don't talk about very much:  security.

We've had a couple of high-profile hacks on power grids recently.  I'm unconvinced that the software security issues for renewables are any worse than those for fossil fuels or nuclear.  But what if a state or non-state actor embarked on a coordinated sabotage campaign?

It's relatively hard to bring down power lines, and power networks are relatively robust.  Switching stations are small and can be effectively guarded.  Generating plants are already already well guarded, and the cost of attacking them would be high for any organized group of saboteurs.  Dams are hard to destroy without specialized explosives, and they're easy to guard.

Solar and wind farms are kind of a nightmare, though.

First, they're big.  They consume a lot of area.  They require a lot of fencing to secure.  In many cases, the fencing has to accommodate public and private rights of way.  And even if you have the fencing, guarding it will be hugely expensive.

Once you get through the fencing, you can take out solar panels with a hammer.  Or a sand blaster.  Or acid.  In some cases, exploding some sort of corrosive agent over a solar farm could degrade a significant chunk of it all at once.  How hard would it be to rig a couple of drones to spray hydrofluoric acid down a row of solar panels?

Wind farms are a little harder to take out with low-tech sabotage, but they're even more distributed than solar farms.  And wind turbines have much higher power density per localized area.  It doesn't take much explosive on a wind turbine pillar to take out more than a megawatt of nameplate capacity.  And what happens if you fly a drone into a turbine blade, at just the right spot, with just the right hardware, to inflict maximum damage?

Rooftop solar might be a bit more immune from sabotage.  But how many solar panels do you need to take offline before the power company has to make big changes to the external power delivery to a neighborhood?  And I'm still unconvinced that the bulk of residential power is going to come from rooftops, especially in cities.

One of the nice things about coal, gas, and nuclear is that they are generated indoors, with hefty buildings surrounding them, with simple fencing and easy tasks for guards.  Wind and solar must be sited outdoors, with fragile generation mechanisms.  We should think through the security issues carefully.

Friday, April 3, 2015

The Iran Nuclear Program and the Boiling Frog Syndrome

The framework is out for the Iran nuke deal, and the shrieking has begun.  However, based on a little arithmetic that I'm kicking myself for not having done about four years ago, the deal may--now--be the best we can do.

From the framework, it is asserted that Iran currently has 19,000 centrifuges deployed and 10 tonnes (metric tonnes, each equal to 1000 kg) of low-enriched uranium (LEU).  I knew about the 19,000 centrifuges, but the 10 tonnes of LEU took me be surprise.  And it's the cause of the self-kicking.

It turns out it's a lot harder to take natural uranium (NU), which is about 0.7% U-235 and enrich it to 3.7% LEU than it is to take 3.7% LEU and enrich it to 90% highly-enriched uranium (HEU).  Here's a handy blurb on how it's done, but the key graph, reproduced below, is the second one:

This takes a little explaining.

First, we're dealing with a standard metric of how much energy it takes to separate a given amount of feed stock uranium of a particular assay to a product stock of a particular enriched assay, called a separative work unit (SWU).  Reading the definition will make your head hurt, but the SWU is very handy, because it tells you how much spinning of centrifuges has to happen to get to a certain level of enrichment.  And if you know how many SWUs a year a particular centrifuge can produce, you can figure out what the enrichment capacity is.

The IR-1 centrifuges that make up most of Iran's separation capacity did about 0.7-0.9 SWUs per centrifuge per year by the end of 2011, and I'd guess that performance has improved somewhat in the intervening three years.  It's gonna be a little less than 1 SWU/year-centrifuge.  I'm going to call it 0.9 SWU/year-centrifuge but remember that that number is an educated guess.

But back to the graph above.  This is the enrichment curve for 1 tonne of NU feedstock.  The horizontal axis is the enrichment level that that uranium has reached, and the vertical axis tells you how many SWUs you have to apply to get there.  Labeled along the curve are some key milestones for typical LEU (4%, although we're going to eyeball that back to 3.7% in a moment, because that's what the agreement implies), and the amount of enriched product stock you get out of that original 1 tonne of feed.  The rest of the stock is assumed to be "tails", or "depleted", meaning that it's had most of the U-235 removed from it (somewhere about 0.2% U-235).

Note that it takes about 800 SWUs to turn the 1 tonne of NU feedstock into 133 kg of 3.7% LEU, but it only takes another 500 SWUs to turn that 133 kg of LEU into 5.6 kg of 90% HEU, fully capable of going boom.

That sounds weird. Why does it take fewer SWUs to make the stock much more enriched?  The answer lies with the amount of material you're enriching.  You go from 1 tonne of NU to 133 kg of LEU, and then to only 5.6 kg of HEU.  The SWUs are work amount on feedstock.  If you consider the LEU to be the feedstock for HEU, rather than NU, then the fewer kilograms to work on means less work for more and more enrichment.

So, to get 1 kg of HEU from NU, you need to put in 232 SWU/kg.
But to get 1 kg of HEU from 3.7% LEU, you only need to put in 89 SWU/kg.  Call it 100 SWU/kg.

Another thing to note:  Enriching from NU to LEU reduces the amount of product by a factor of 7.5.  Enriching NU to HEU reduces the amount of product by a factor of 179.  But enriching LEU to HEU only reduces the amount of product by a factor of about 24, which we will round off to 25 for ease of use.

So how much 90% HEU do we need for a bomb?

The Little Boy bomb dropped on Hiroshima was a "gun-type fission weapon", and it required 64 kg of 80% HEU.  Using conventional cannon technology, it fired a hollow cylinder of HEU over a thinner cylinder of HEU that fit just inside the hollow, to create a critical mass in the world's nastiest game of ring-toss.  It had a yield of about 15 kilotons.

The Fat Man Nagasaki bomb used plutonium in an "implosion" configuration.  In this, shaped charges went off to liquefy, then compress, a solid sphere of plutonium.  Harder to do, but it requires less material, and it generates a better yield.  Fat Man yielded 21 kilotons using 6.2 kg of Pu-239.

Turns out that you can build implosion weapons out of HEU as well, and the state of the art requires a lot less material.  This paper examines three different implosion technologies for both HEU and Pu bombs, labelled "low-tech" (equivalent to Fat Man technology), "medium-tech", and "high-tech".  The "medium-tech" scenario, of which I'd think we'd have to assume a country like Iran was capable, requires only 9 kg of 90% HEU to produce a 20 kiloton bomb, equivalent to what was used on Nagasaki.

Now let's go back to our 10 tonnes of Iranian LEU, and 19,000 centrifuges:
  • 10,000 kg of 3.7% LEU / 25 LEU-to-HEU factor = 400 kg of 90% HEU.
  • 19,000 centrifuges * 0.9 SWU/yr-cfuge = 17,000 SWU/yr.
  • 17,000 SWU/yr / 100 SWU/kg = 170 kg/yr of HEU.
  • That's 14 kg/month of HEU.
  • So, assuming Iran has a bomb design ready to go (a conservative bet), it could enrich its whole stock of 10 tonnes of LEU and produce 1.5 Nagasaki-sized bombs a month, for two and a half years, ending up with 44 bombs.

Holy shit.

Iran can break out whenever it wants.  It can have 3 bombs, one to test and two to deploy, in two months, give or take some machining and assembly time.  If the IAEA comes to inspect once a month, one trumped-up excuse to force it to skip a visit is all the wiggle room they need.

Based on that, a deal that limits Iran to about 5000 centrifuges and 300 kg of LEU on-hand sounds fuckin' awesome.

But even with the deal, the "one year break out" is silly:
  • 300 kg of LEU / 25 LEU-to-HEU factor = 12 kg of 90% HEU
  • 5000 centrifuges * 0.9 SWU/yr-cfuge = 4500 SWU/yr.
  • 4500 SWU/yr / 100 SWU/kg = 45 kg/yr of HEU.
  • That's 3.75 kg/month of HEU.
  • We can't use the same 3-bomb criterion for a break-out, because there isn't enough LEU to support 3 bombs' worth of HEU.  But a 1-bomb break out would take 2.4 months.
That doesn't sound like "more than a year" to me.  You can argue whether one untested bomb constitutes a break-out, of course.  But consider the following two game propositions:
  1. If I respond to a breakout, I run a risk that the one bomb will be successfully used against me.  Upside: better foreign policy leverage = medium.  Downside * probability of downside: Huge times kinda small = medium.  Downside-to-upside ratio: 1.
  2. If I don't respond to a breakout, there is no risk that the bomb will be successfully used against me.  Upside:  Maybe the horse will sing = small.  Downside * probability of downside: foreign policy hemmed in * medium probability = medium.  Downside-to-upside ratio:  less than 1.

But I digress from the main point by pointing out that even the fuckin' awesome deal isn't so fuckin' awesome.  And the main point is this:

How for fuck's sake did we allow this to happen?

Let's go back to the IR-1 centrifuge performance blurb.  There we learn (fig. 1) that Iran had only 7000 centrifuges in May, 2009, and this NYT article states that Iran had about 1 tonne of LEU in February of 2009.

Let's run the numbers:
  • 1000 kg of LEU / 25 LEU-to-HEU factor = 40 kg of 90% HEU
  • 7000 centrifuges * 0.6 SWU/yr-cfuge (based performance estimates cited above--yaaaay Stuxnet!) = 4200 SWU/yr.
  • 4200 SWU/yr / 100 SWU/kg= 42 kg/yr of HEU.
  • That's 3.5 kg/month.
  • Using the 3-bomb breakout criterion, that's a 7.7 month breakout time.
So, being charitable, the Obama Administration's "deal" pretty much undoes the damage they allowed to happen on their watch.

So how did we get to 10 tonnes and 19,000 centrifuges?

Well, I have to admit that I feel pretty stupid for not running these numbers back then.  There's no magic here.  But the real answer appears that the administration was... really vague, in a happy-talk kinda way, without ever actually lying its ass off:
If Tehran has no hidden fuel-production facilities, to create a bomb it would have to convert its existing stockpile of low-enriched uranium into bomb-grade material. International inspectors, who visit Natanz regularly, would presumably raise alarms. Iran would also have to produce or buy a working weapons design, complete with triggering devices, and make it small enough to fit in one of its missiles.

The official American estimate is that Iran could produce a nuclear weapon between 2010 and 2015, probably later rather than sooner. Meir Dagan, the director of the Mossad, Israel’s main spy agency, told the Israeli Parliament in June that unless action was taken, Iran would have its first bomb by 2014, according to an account in the Israeli newspaper Haaretz that Israeli officials have confirmed.
It's hard not to come to the conclusion that things were pretty bad when Obama took office, and now they're not only bad in a "Waaaahhh, Iran's going to destabilize the region" kind of way; now it's more like "Oh shit oh god, Iran could have a strategic nuclear capability in about two years".

I've been pretty sure that Obama and Clinton's booting of the Status of Forces Agreement for Iraq was the single worst foreign policy blunder of the administration--until now.  This situation's gone from a grease fire in the kitchen at the beginning of Obama's tenure to a five-alarm fire.

Make no mistake:  the deal, if it actually gets done, is not only pretty good, it is now existentially necessary.  But it should never have come to this.  Like the frog that sits in the pot of water and slowly boils to death, we just assumed that the constant accumulation of stockpile and capacity would never make a qualitative difference.