Category Archives: Spacecraft a Week

I’ll design a new spacecraft every week. Then I’ll blog about it.

Lunar Xistera II

Our Lunar Xistera provides a means for a spacecraft to land on the moon with no propellant—just brakes. Can we take off the same way?

Not quite. Braking is comparatively easy. Dissipating that energy is a thermal problem, at worst. Taking off again is another matter. It requires energy to be stored and then imparted to the spacecraft. Both of those requirements lead to a heavier spacecraft or some more subtle infrastructure on the moon. So, can we avoid expending all this energy? Can we store up momentum in the spacecraft as we land and pay it back as we lift off without expending energy? It may just be possible.

First let’s take a look at a straightforward design that includes batteries and electric motors. Wire up the motor to the battery and accelerate like an electric car. A lunar Prius.

Now, remember that to use that same lunar runway, the spacecraft needs to accelerate at 5g. It would begin its run-up to liftoff at the more tightly curved end of the runway, which is where the vehicle stopped after landing. (That makes a certain intuitive sense.) This 20,000 kg spacecraft has to reach 1679 m/s, the velocity for a circular lunar orbit that is just barely above the surface of the moon. For a constant 5g, the power is at its maximum at the end of the runway, where the speed is enough for the spacecraft to be in orbit. At that instant, the power is over 1.6 GW, more kick than Doc Brown needs for his flux capacitor. And the spacecraft has acquired over 28 GJ of kinetic energy during its short trip. Even if you wanted to use that many batteries and an appropriate electric motor, that hardware alone would weigh more than the 20,000 kg vehicle. Sorry, but this design is just too far out of reach of current technology. Even for Spacecraftlab.

Before giving up entirely on motors, let’s consider a more subtle approach based on gyroscopic effects. It turns out that you can impart angular momentum (i.e. apply torque) to a mechanical system in many ways. Some use less energy than others. This fact is quite profound, drawing a really useful distinction between energy and momentum, and it’s at the core of how power-starved spacecraft rotate quickly in orbit.  A space technology that is particularly good at minimizing that energy is the control moment gyroscope (CMG). A CMG consists of a spinning rotor that tilts on a gimbal. That tilting motion imparts torque with hardly any change in kinetic energy—in other words, without much power. For the power of a few light bulbs, a CMG can produce enough torque to tip over a car. Seems promising, right?

For this design to work, that torque has to be parallel to the axle that spins the wheels. However, as a single CMG gimbals, the direction of its torque rotates too. That effect could cause the spacecraft to flop around on the runway like a fish on land as the CMG rotates, which is not at all what we want.

A pair of CMGs that tilt in opposite directions can cancel the off-axis component and leave only the torque we want. “Scissored pair” is the name for such an arrangement. This video shows a scissored pair.

The red lines are the angular momentum vectors of each individual CMG and their sum. Notice that the sum of those vectors is always along a single line (vertical in the video, horizontal in the case of our spacecraft). That’s also the direction of the torque. Unlike a single CMG, whose torque tilts with the gimbal in an inconvenient way, a scissored pair applies torque along this single, constant axis, such as the axle of a vehicle with wheels. If we ditch the motors that drive the gimbals, replacing them with a torsional spring that pushes the pair of rotors apart, there would be no electrical power required during takeoff other than to keep the CMG rotors spinning. And that’s certainly a desirable feature, since power is in such short supply on the moon, and since batteries to store it are heavier than we would like. Incidentally, that spring is beefy. I’d say about 320 kg of carbon steel.

Here’s some engineering that describes what a CMG-powered spacecraft would have to look like if it is to lift off the lunar surface on the runway we’re thinking of.

Each of the CMGs lies on an axle that freely rotates. The rotors start out with angular-momentum vectors parallel to each other and parallel to the wheels’ axis of rotation. Each gimbal then tilts about 180 degrees as the spacecraft travels along the runway. As they do so, they impart angular momentum along that axle to drive the wheels, which we assume are about 1 m in radius, as discussed in the earlier Lunar Xistera post. When the scissored pair has gimbaled to its 180 deg limit, the angular momentum in the pair of CMGs has been imparted to the spacecraft. Here, the spacecraft can be considered to have angular momentum referenced to a point like the end of the runway. The point doesn’t really matter, but picking one makes the calculations simple. The angular momentum consists of the spacecraft’s mass traveling at its velocity, at a radial distance from the ground equal to the wheel radius. That’s a mouthful. Have a look at this picture to see what I mean about the angular momentum (H) of the vehicle.

CMG_takeoff+crop

To accomplish this extraordinary goal of an unpowered liftoff from the moon, we’ll need two 1.45 m radius, rim-weighted rotors that weigh over 4500 kg each (that’s nearly 50 times the size of the Space Station’s CMG rotors), much larger than any CMG I’ve ever encountered. And because they’re larger than the wheels, we’ll need a transmission that offsets a central part of the axle from the wheels, allowing the CMG assembly to rotate without hitting the ground. The CMG assembly drives the wheels with some sort of belt or gear arrangement. Each rotor needs to spin at 12,000 RPM, which is very sporty, and probably beyond the capability of the best steel: the tensile stress in this material will be high, and the rotors are likely made of some exotic material. Let’s also say that the rotor constitutes 66% of the mass of each CMG, which is also quite optimistic, given that the Space Station’s CMGs are only 37% rotor, 63% other hardware.

CMG_drivetrain_front

Front view of the CMG drivetrain (sectioned through the middle)

CMG_Drivetrain_side_view

Side View of the CMG Drivetrain (Wheels and Axles Shown As Semitransparent)

Spacecraft with Side View of Drivetrain Shown

The top figure (above) is a sketch of this drivetrain, viewed from the front or rear. It consists of a scissored pair of CMGs, interconnected with a worm gear and two spur gears. Some other mechanical solution may be better; this is simply what occurred to me. The next figure is a side view, and the last shows that side view where it belongs in the spacecraft. You’ll notice that the CMG assembly is offset from the wheels’ center of rotation. You’ll also see a torsional-spring arrangement that connects the worm gear to a support structure of the CMG assembly. A pulley & belt connects the CMG assembly to the wheel axle. Maybe gears would be better there, considering the mechanical power involved. Whatever. It’s the big picture that matters.

The animation below includes some gray material that indicates how the spacecraft chassis would mount to these rotating assemblies.

With these admittedly sketchy assumptions, about 6300 kg of mass remains for the rest of the spacecraft: payload, wheels, structure, guidance components, and so on. Yes, you’ll need to spin up the rotors (it could take hours, even days, from a standstill). You’ll need to plug in the spacecraft at some point, or let its own solar panels provide that power. Also, I should point out that this design has virtually no margin to account for friction and other losses from rolling on the runway and from gears meshing within the drivetrain, which could well double the requirements.

HOWEVER, if you could build such a contraption, you would be able to lift off of the moon without significant electrical power (remember the spring), without propellant, and probably with fairly small batteries. That’s incredible!  Seems like this concept deserves a closer look.

Consider the upside: a spacecraft could land on the moon and use a kind of mechanical wind-up toy technique to tension that spring. As the vehicle slows, the spring winds up, and it tilts these huge CMGs as they suck up the momentum of the vehicle on the runway. As long as the rotors continue to spin, the spacecraft is ready to take off at a moment’s notice (well, maybe with a little rocket-motor or battery-driven help to account for friction that assists landing but retards take-off).

Stepping back, I’d guess that this concept is on the ragged edge of possible, certainly not easy. But that’s what this blog is about, after all. Innovation demands that we reject conventional wisdom, such as the belief that we need rockets to land on the moon and take off again. It happens when ideas collide in an unexpected way. It happens when we know the rules just well enough to break them but not so well that they become dogma. And in my opinion, we innovate when we sense a worthwhile goal just out of reach, a goal like economically viable lunar commerce. That sense of possibility inspires us to investigate the unfamiliar.

No fuel, little power, and indefinitely reusable. Now that’s sustainable lunar transportation.

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All You Need Is Water

water_messier_81

Water, water, water. It’s essential for human settlement of space. Its uses are legion. Astronauts need water to drink. Permanent settlements beyond Earth will require water for crops, medicine, and washing. Water serves as an excellent liquid radiation shield. Or freeze it and use it as a structural material. Water, or ice, can bind other materials, for example producing mud bricks for construction in space. Water-soluble materials might be 3D-printed. Water efficiently, safely, and conveniently stores hydrogen and oxygen for use as rocket fuel. If we remove the oxygen from water—to breathe it—the leftover hydrogen can combine with carbon to produce methane, another rocket fuel and, in liquid form, an even better radiation shield. Water is the basis for batteries known as fuel cells. Water can be a coolant, a lubricant, and a hydraulic fluid.  And it’s non-toxic. Use the water for all of the above, trading off among them as necessary.

In my opinion, if we are to become a spacefaring species, we must direct our exploration architectures, our space technologies, and our scientific investigation of the planets toward a sustainable and coherent vision for space exploration centered on using the resources that are already in space. Chief among these is water.

In the spirit of Spacecraft a Week, let’s think about a single spacecraft that could exploit this abundant resource: a robotic spacecraft that explores asteroids, refueling as it goes.

It’s easy. All you need is water. And water is on the moon, on asteroids, and on Mars. Saturn’s rings are mostly water. Europa has oceans of it.

What makes this design possible is a water-based propulsion technology that Rodrigo Zeledon is developing at Cornell University. His is not the only one. Tethers Unlimited Inc. has done a great job with a related technology. In fact, the basics were well understood decades ago. What has changed is the rise of small satellites and the advances in fuel-cell technology, both of which we can now infuse into new space systems that haven’t been seen before. We expect Rodrigo’s solution to be uniquely mass and volume efficient thanks to a new flight-dynamics concept and simplifications. It would be capable of accelerating a 3U CubeSat by 1000-2000 m/s, unheard of in the early days of space exploration.

A brief aside about Rodrigo’s breakthrough research. The spacecraft has a water tank, where an electrolyzer from a fuel cell uses solar power to separate oxygen from hydrogen. The resulting gas has been given many names over the years. Let’s call it Zeledine. The electrolysis continues until the pressure in the tank reaches about 10 atmospheres (maybe higher in some applications). After that point, whenever the mission calls for thrust, the spacecraft can open a valve that sends some Zeledine into a combustion chamber. The valve closes, a spark plug ignites the gas, and the two reunite as water, shooting out the rocket nozzle with very high efficiency.

Unlike typical electric propulsion systems, there is no need for a battery to store energy. The water itself stores that energy. Unlike cryogenic oxygen/hydrogen propulsion, this technology doesn’t need heavy insulation, cryo pumps, or other hardware associated with keeping the separate oxygen and hydrogen as super-cold liquids. This propellant—water, remember—can be stored indefinitely and even transferred to some other spacecraft with the help of mundane terrestrial technology. And unlike the fuel in other propulsion techniques, the Zeledine is stored as a single fluid, kept separate from the water in the tank by the spin of the spacecraft, just like samples in a centrifuge. That spin has other benefits. It helps cancel out misalignments of the rocket nozzle, gyroscopically stiffens the spacecraft so that a little torque imbalance from the rocket doesn’t tip it over, and guarantees safe and reliable flight dynamics.

Here are some pictures that may help explain how this works on a 3U CubeSat, where one gram of water at a time combusts to produce half-second pulses of thrust.

 

3u_spinner  3ucubesat_cutaway

3U CubeSat with Electrolysis Propulsion.  Left: spinning spacecraft; right: cutaway view

But I have in mind something larger than a CubeSat. This asteroid explorer would be about the size of the brilliantly successful Hayabusa-1 spacecraft, which famously retrieved samples from the Itokawa asteroid a few years ago. Its mass was 530 kg. That spacecraft was able to visit an asteroid, with the help of an Earth-flyby gravity assist, and bring back a sample. It did so with 65 kg of xenon for its ion-propulsion system and another 50 kg of chemical bipropellant for attitude control. It used only 22 kg of that xenon.

For this asteroid explorer, I’ll trade in the 20 kg (or more) that Hayabusa dedicated to its sample return capsule for a drill, a heater, and a hose to melt ice and pump it into the propellant tank. Yes, ice can be found on some asteroids, including Themis (Itokawa, not so much, by the way). We’ll use that subsystem to refuel the spacecraft after it lands.

And I’ll also swap out the three tanks—xenon, monomethyl hydrazine, and nitrogen tetroxide—for one water tank. The Zeledine can serve both to change the orbit (where Hayabusa used xenon) and to impart reaction-control torques (where Hayabusa used MMH and NTO).  Let’s guess that Rodrigo’s solution would need only half of the 70 kg mass of Hayabusa’s electric propulsion subsystem and about the same mass again for its 12 attitude-control jets. Furthermore, we won’t need the roughly 6.8 kg power-processing unit. I also suspect we’ll need fewer batteries than Hayabusa, but let’s leave them alone just for some mass margin. We’ll also keep the solar arrays, which can provide 1400 W to Hayabusa’s propulsion system, along with the rest of the spacecraft. And we’ll design our system to match Hayabusa’s roughly 1250 m/s velocity-change throughout the mission.

Remember, it did so with only 22 kg of xenon propellant. We’ll need a lot more because xenon ion propulsion is much more efficient than water propulsion: it offers a specific impulse of 3000 sec, while ours is about 300 sec. But we save a lot in other hardware. Conservatively, about 218 kg is now available as water storage. That figure neglects efficiencies gained in the tank, which needs not be pressurized as much as Hayabusa’s, and in general plumbing and mechanical bits. Thanks to those mass savings, it turns out we need only another 53 kg of water to achieve the same propulsion performance. The tank volume would have to roughly double, in part because xenon and bipropellant are denser than water, but that’s merely an increase in linear dimensions of 28%. At such low pressure, the tank doesn’t have to be spherical to be mass-efficient, unlike high-pressure propellant tanks one finds on typical spacecraft. So, these water tanks can be any old shape, whatever fits in the unused nooks within the Hayabusa structure.

If Hayabusa could make it all the way to Itokawa and back, I believe this design could make it to the asteroid belt as well but survey asteroids continually, reporting back to Earth when it finds something valuable. I don’t know, platinum group metals, perhaps? DNA? Water, for sure. Some day, NASA may be in the business of buying water from commercial entities, as some entrepreneurs hope. Such purchases are not in NASA’s current plan, but I argue that we need to think quite a bit bigger than the individual spacecraft that we discuss when we talk about space exploration. We need more than a flexible path.  We need a sustainable path, a paradigm that ends our reliance on mass sent from Earth. 

There’s nowhere you can be that isn’t where you’re meant to be. It’s easy. All you need is water.

LEOHive

leohive1

Modestly sized structures in space can be diaphanous. That’s because they’re not subject to particularly powerful gravitational effects or other forces. This fact enables contemporary geostationary satellites to deploy solar arrays longer than the wingspan of a 737 that weigh only a few hundred kg. So why spend weight on making them strong? One reason is that the process of in-orbit assembly might require it. Partly built structures may collapse unless they’re strengthened during the construction process.

These forces can be large in the case of large structures. For example, they can be strong enough to prevent the construction of space elevators with any conceivable materials. So, what if we work with the orbit mechanics instead of against them? It turns out that we could construct very large space structures that can be assembled with the help of spaceflight physics. Let’s look at one example, which I’ll call a LEOHive, to suggest its use as a large-scale habitat in low Earth orbit.

The key innovation here comes from research that Ben Reinhardt and I are conducting at Cornell. We found this interesting principle that tells you where it’s safe to stand on the outside of the space station, among other things. I mean “safe” in that you, as an astronaut, can stand with your feet planted on certain surfaces while the physics of orbits presses you into that surface, albeit very gently. That’s awfully good to know if you find yourself in a Sandra Bullock sort of situation or if you’re just interested in wing-walking.

By the way, those of you who are already fans of the Clohessy-Wiltshire equations will wonder if there’s anything new to this. I’m telling you that both Ben and I have looked, and we can’t find any references that talk about reaction forces on the surface of orbiting bodies, despite that it’s a very simple consequence of these venerable equations.

northsouthorbits

To be clear, two objects in orbit don’t attract one another because of a gravitational pull between them. Let me explain with a thought experiment that involves two astronauts. Say they’re both orbiting in the same circular orbit, more or less around the Earth’s equator. An equatorial orbit lets me say “north” and “east,” and you’ll know what I mean, but the same principle applies regardless of where above the earth these things orbit. Let’s tilt one of the orbital planes away from the other, but keep it identical in every respect. Once they’re in these two intersecting orbits, the two astronauts encounter each other twice per orbit. If one begins north of the other, he or she will eventually pass the other astronaut toward the south, and back up again half an orbit later, forever. The figure above shows these two paths.

Here’s where the Reinhardt principle comes in. If the southerly astronaut extends an arm up to the northerly astronaut, the northerly one can stand on it. The arm reacts the forces that would tend to pull that astronaut southward, without the need for the bottom one to grip the top one at all. In this case, both astronauts now travel on a single circular trajectory that averages the two earlier orbits. If they ever lose contact, they’ll return to their north-south dance.

astronauts

The Reinhardt principle applies to many more situations than only this north-south oriented pair of objects in orbit. In fact, Ben has come up with equations and a convenient picture that shows where, on the surface of an orbiting sphere, an object always feels some inward acceleration. He’s also working on a 3D plot that shows all the places on the International Space Station where something can park in this way.

In particular, the Reinhardt principle simplifies building a large, delicate structure in Earth orbit. It tells you where to place elements of this structure relative to a perfect circular reference orbit so that the components stay put while the glue dries, cement hardens, epoxy cures, genetically modified lichens grow, water freezes, astronauts attach 3D printed rivets, what have you.  Here are the rules:

  • Any component that we place above or below a surface—again, in this north-south sense—wants to press itself into that surface.
  • Any component we place inside or outside a surface—in the direction toward the Earth or deep space —wants to accelerate away from that surface. However, a component placed on the Earthward side of a surface that is outside the orbit (toward deep space) wants to stay on that side, as does its counterpart placed on the spaceward side of a surface that is Earthward of the reference orbit.
  • Any component that we place ahead of or behind a surface—in the east-west sense—feels no need to accelerate toward or away from the surface at all. However, all these rules apply simultaneously. So this rule in combination with the others still allows us to adhere components to one another.

So, consider a sort of rover that assembles truss elements or other large components. It does so autonomously, moving from component to component, adhering them together and moving on while some time-consuming chemical process hardens the structure. Again, that could be any one of a number of ways to adhere structures together. The LEOHive built this way takes shape first in a north-south direction and then extends outward in the other two dimensions leaning on interlocking connections made possible by the placement of earlier components.

Quite a few subtleties remain. As the structure takes shape, its mass distribution should conform to the principles of gravity-gradient stabilization. Long story. Ask me another time. Also, as the rover adds components, the mass center shifts, possibly changing how the rules apply across the structure. Planning the assembly to accommodate these subtleties doesn’t seem like a show-stopper to me, although coming up with a general algorithm will require the attention of at least one interested graduate student.

We do the same sort of thing on Earth, although we don’t typically think very hard about it. We assemble buildings from the ground up, parallel to gravity, because it just makes sense that way. The Reinhardt principle provides the insight we need to establish an analogous process for in-orbit construction.

Dust off the Moon

regolith_rocket

A ready and ample supply of propellant in space sure would be useful, on the Moon or Mars, particularly. What if we could use regolith—the sand or dust present on planetary surfaces—as a propellant, directly? Would a spacecraft accelerated by dust even lift off the surface? If so, could this technique serve as a means of transport from point to point on the Moon?

Maybe you’ve already encountered the idea of a regolith rocket, which is not quite what I’m talking about. But let me describe it anyway. A classic regolith rocket involves preheating the regolith to give it some additional energy and then mixing it with a high-pressure gas. As the expanding gas flows out of the spacecraft, it sucks in and transports, or “entrains,” the regolith particles, thus producing thrust. It’s very similar to a sandblasting machine.

That’s all well and good, but you need to bring that gas with you, perhaps from Earth or from some mining operation off Earth. Once it’s used up, you’ll need to replenish the gas.

I think we can do better. Specifically, we can accelerate the regolith without any entrainment, without adding a gas. A vehicle with such a propulsion system could take off and land repeatedly without needing to recharge a tank of working fluid. It would scoop up dust to refuel. That’s all.

How would such a regolith-only propulsion system work? I propose a design that uses a mechanical pump—a fan or turbine—that expels the regolith from the back of the rocket as the propellant. Let’s consider the specific case of a lunar transport. Clearly there’s no lunar air with which to blow the regolith through the rocket. I’m thinking of a turbine that mechanically accelerates the regolith that falls into it from a hopper, or a tank, thanks to gravity. Unlike a classic regolith rocket, the regolith here provides all the mass flow, and a source of power on the spacecraft provides all the energy to spin the turbine.

Here’s a potential problem. In the process of moving the regolith through the turbine, the blades might ablate somewhat. So, one goal would be to choose a material for those blades that is tough enough to withstand all this internal sandblasting for the duration of liftoff and landing. However, it turns out that if the dust can be sifted down to particles of 20 microns or smaller, we don’t need to take any extraordinary measures. Even terrestrial turbine blades aren’t damaged by such tiny grains. They carry too little energy to impart stress in the blades beyond the yield strength of the material.

Another issue: how do we get the regolith into the turbine? You have to fill up the tank somehow—a shovel and a sieve?—but then mere gravity feeds the regolith into the fan, just like it pulls sand through an hourglass. As the spacecraft lifts off and accelerates further under the power of the engine, the mass flow rate could be allowed to increase naturally or could be throttled back with an adjustable aperture, depending on which is more efficient.

Now let’s look at a design that may support lunar businesses, i.e. commerce among Moon bases. I’ll describe the design of a printer-size transport vehicle: 10-20 kg total mass. Sure, there is probably some economy of scale that would make a larger vehicle more efficient. But let’s take this small example to be an existence proof for a larger one. Also, this little one is inexpensive enough that a person might actually build and test a prototype in the near term. (Or maybe someday Amazon will want to deliver little packages via drones on the Moon, too. They’ll see the wisdom in this idea and will come knocking at the door of my lab at Cornell looking to sponsor the research. One can dream.)

Let’s first consider a lunar transport design that offers very low specific impulse (abbreviated Isp, a measure of the efficiency of propulsion). This transport hops, if you can call kilometer-scale trajectories “hops.” The engine expels propellant at 0.14 kg/s and lifts off at an angle of 45 deg. to the vertical, which optimizes the trajectory for distance. It accelerates until it reaches maximum speed at an altitude of about 540 m. Doing so expends about 74% of the propellant, at which point the engine shuts off. The transport continues to coast ballistically, through a peak altitude of 940 m, and then drops down to 390 m altitude, at which point regolith is fed into the turbine once more. Applying that final thrust slows the descent, and the vehicle comes to a stop at the surface of the Moon. It lands 3.7 km from its starting point, if it’s carrying no load. The flight takes only a minute or two. Carrying a payload means sacrificing some of the regolith propellant, so that the total mass can still lift off. And less propellant leads to shorter trajectories, of course.

The vehicle is designed to carry 13 kg of propellant, which is enough to accomplish these hops. The rocket equation tells us that this 0.14 kg/s mass-flow rate, with an exit velocity of 240 m/s, leads to an Isp of 24 seconds. That Isp would be shamefully low for a chemical propulsion system, where Isp is typically in the hundreds of seconds. But remember—the propellant is everywhere you look. A scoop and a sieve constitute the gas pump here. This convenience comes at the cost of efficiency, but I think it’s a good trade for this particular concept.

Limitations on the speed of the turbine ultimately drive the design. The speed at which a turbine rotates is limited by the tensile strength of the material that it’s made of, as well as the bearings that support the rotating portion. The AMT Mercury small turbine for unmanned aircraft, for example, is designed to rotate at 151,000 RPM. Let’s base our Moon transport design on this turbine, but I’ll assume that we can boost its rotation by about 20%, for 181,200 RPM. It will need considerable redesign so that the flow is straighter, since the goal here is not to compress gas but simply to accelerate the particles. But I hope that this example suffices as an estimate of the weight. They say it’s about 2.2 kg for this great little turbine.

We’ll model the turbine blades so that the twist along the blade length reaches 45 deg. halfway along each blade. Using two turbine stages might be important so that the expelled propellant doesn’t carry significant angular momentum, which would be in the same direction as the rotation of the turbine that imparts its axial velocity. That momentum would cause the vehicle to spin up in the opposite direction, and that spin would be difficult to dissipate before the vehicle lands. This simple model has the propellant exiting the turbine stage(s) at an axial velocity equal to that of the blade midpoint in the plane of its rotation: i.e. the dust bounces off the 45 deg. angled blade and acquires an axial speed equal to the blade’s lateral speed when they were in contact.

As the regolith passes through the blades, it tends to slow down the turbine. The power required to keep this turbine spinning is roughly equal to the change in energy of that accelerated dust. With a mass-flow rate of 0.14 kg/s, accelerated to 240 m/s, the change in kinetic energy (or power) is 3.98 kW. Let’s use a 4 kW electric motor to provide this power. A nice brushless DC one is available off-the-shelf and weighs only 3.3 kg. We’ll also need a transmission of some kind that gears up the 8000 RPM peak rate of the motor to the 181,200 RPM that the turbine demands. Prof. Brandon Hencey at Cornell tells me that some aircraft-engine turbines, e.g. from Pratt and Whitney, include a transmission that reduces speed, sometimes for noise purposes. Our vehicle would use a similarly designed transmission but run backwards so that the gear ratio allows the motor to drive the high-speed turbine.

Batteries. Ah, batteries. It is my belief that the highest-priority technology advance for space technology is increasing energy density (J/kg) and power density (W/kg). So many extraordinary systems would be enabled if arbitrarily large energy storage were possible and if it could be expended as power arbitrarily fast. That technology development is not necessarily NASA’s responsibility, though.  Using commercially developed technologies might be the fastest way to see improvements. Today the best lithium-ion batteries provide about 360,000 J/kg. They’re very slow to discharge, i.e. to expend their energy. That discharge rate is limited to 10-15 A, which means that the energy drools out over the course of half an hour or longer. The 13 kg of propellant in this design has to be expelled over the course of only 93 seconds. So, ultracapacitors are better choices than batteries here. They’re less mass-efficient in storing energy (only 230,400 J/kg) than lithium-ion batteries, but they can discharge quickly enough to impart the power that the motor demands. These ultracaps total about 1.6 kg. Another alternative would be flywheel energy storage. Interesting as it may be, this technology is not much more appealing than high-performance ultracaps when you take into account the hardware necessary to make the system work.

The motor, batteries, turbine, transmission, electrical harness, mechanical components, and propellant of our lunar transport total 18 kg. The thrust available from the engine is 34 N, which means that the 20 kg vehicle taking off in lunar gravity has another 2 kg available for everything else: tank, structure, guidance sensors, solar cells, flight computer. That’s not much, perhaps, but remember that the “tank” is just an unpressurized bucket, and other than the batteries discharging, there is no thermal activity on this vehicle to require special materials, insulation, et al. This tank needs to hold 13 kg of regolith powder, which (at 1800 kg/m3) could fit in a cube 20 cm on a side. And the electronic guts of a CubeSat (no more than 0.5 kg worth of boards and solar cells) should be sufficient for the rest of the electronics.

One more thing. This spinning turbine will take time to reach full speed. There is likely a lot of kinetic energy stored in the turbine itself. I propose that solar power be used to charge up the ultracaps and spin up the turbine while it’s on the ground, without expending energy from the batteries that would be indispensable in flight. Once it’s spinning, a single-stage turbine would helpfully store angular momentum that gyroscopically stiffens the attitude in response to disturbances, such as misalignments of the rocket engine or liftoff and landing perturbations.

This low-Isp design is based on a 2.5 cm radius turbine, in which the regolith impacts the blades at, on average, about halfway along their length. Now, let’s consider a higher-Isp design. A 4 cm-radius turbine gives the regolith higher exit velocity: 380 m/s instead of 240 m/s. However, for the same 4 kW electric motor, the system is a lot lighter: only 11 kg, of which 4.6 kg is propellant. The higher exit velocity means that more power must be applied to a given amount of regolith, and that requirement limits the total performance. The mass flow rate must drop to 0.055 kg/sec, and the total engine on-time to 83 sec. The upshot is that the trajectory of the higher-Isp design is only about half as high (460 m) and half as far (1.9 km) as the low-Isp vehicle. What we see here is a classic trend in propulsion design: that you pay a power penalty for higher efficiency. And that’s why in-space propulsion is often electric, and launch propulsion chemical. No current electric-propulsion technology can even lift its own weight on Earth. This regolith transport concept lives in a sandy border town between the two.

So, dust off your plans for lunar colonization. Now we have a way to deliver water, rare elements, spools of 3D printer material, and really just about anything to neighboring lunar outposts, in small batches at least. The demonstration-scale vehicle described here may be a precursor to a much more capable, larger transport vehicle. And thanks to bypassing chemical propulsion systems and avoiding the use of refined materials and expendable matter from Earth, we may have found a pretty cheap way to fulfill lunar e-commerce orders.

Tag the Sky

clowes

How about a constellation of small satellites that serve as pixels in an orbiting display?  We could use that for skywriting in orbit.

It turns out that you can see an LED shining from space, at least with binoculars. FITSAT-1, designed by students at Japan’s Fukuoka Institute of Technology, proved it. That spacecraft was an elegantly designed project that shows how clever use of commercially developed technology can inform completely new ideas in spacecraft architecture. In fact, the FITSAT mission opens up the possibility of low-cost optical communications for the masses. At one end—the technological leading edge—NASA’s recent success with the Lunar Laser-Communications Demo sets a high bar for deep-space communications with light. At the other, FITSAT shows what you can do with some elbow grease and some smart students. And I have a feeling they’ll do even better in the years to come.

In fact, FITSAT wasn’t the first to write on the cosmos. Two months before FITSAT launched in 2012, NASA’s Mars Science Lab rovers imprinted the red planet with Morse code that spells out J-P-L. And a decade before MSL, many of us sent our names to NASA for inclusion on the Cassini mission, which carried them to Saturn on a DVD. Maybe it was Carl Sagan and Ann Druyan who started it, sending that gold record into space on Voyager, with the thought that some distant civilization might find it and learn something about our race, by that time likely long gone. But however we might trace this history of writing in space, FITSAT brought home to us the idea that personalizing space and communicating through light is within reach of all of us.

Sure, it’s true that these bright LEDs are a form of light pollution, and astronomers probably aren’t keen on that. However, I would point out that the diodes can be chosen to emit light in very narrow bands, and even in regularly spaced pulses like FITSAT did. That sort of specificity would provide astronomers with a digital means to filter out the LED signals, if there’s a risk that they’ll compromise science. But to the naked eye, these flashing lights can be much more than noise. They can be art.

With dimensions of 10x10x10 cm, and a mass of only 1 kg, many CubeSats can be launched at once. FITSAT itself was part of a group of three 1U CubeSats launched from the International Space Station in one go. This feature confers a very powerful advantage: a constellation of CubeSats can be launched and can begin performing formation maneuvers almost instantly, without needing to catch up with one another the way they would if members of the constellation were launched separately. Some initial activities—maybe a day’s worth or two, at most—and the spacecraft would be ready for operations.

Let’s create a constellation that is basically a matrix of dots, and we’ll take as our guide the venerable Epson MX-80 dot-matrix printer. Its print head consisted of a 9×9 pixel array. So, we’ll need 81 CubeSats for 1980s-caliber printing. How far apart? The Moon subtends an angle of 0.54 deg. in the night sky. And I think you’ll agree that the moon is plenty noticeable. Let’s go for half that width, about 1/4 deg. So, in LEO—specifically, at the ISS altitude of 325 km—the spacecraft would be about 158 m apart.

At this altitude, the constellation flies overhead quickly. The CubeSats orbit the Earth in about 90 minutes, and they’re visible from a given city for not much more than 10 minutes. So, it is tempting to consider what such spacecraft would look like if they were in geostationary orbit (also known as GEO). At that altitude, 35,768 km above the surface, spacecraft in orbit travel as slowly as the Earth rotates. So, this constellation would remain fixed overhead. That’s convenient, but for the LEDs to seem as bright as they do in LEO, they would have to put out over 12,000 times the power. I suppose one would simply use 12,000 as many LEDs, and the spacecraft bus to power them would resemble a high-end geostationary communications satellite. Remember, though, that we are contemplating 81 of these things. At well over a hundred million dollars each, not including launch cost, a constellation of GEO spacecraft would be dauntingly expensive. It would cost about as much as the James Webb Space Telescope, with hardly that level of scientific impact. So, I think LEO is the way to go.

The tricky thing about formation flight is that you can’t have an arbitrary arrangement of satellites travelling with exactly the same velocity. Three subtleties come into play. (1) The spacecraft need to orbit the Earth in the same time; if they don’t have the same orbital period, the constellation drifts apart. But since orbital period isn’t affected by (2) inclination (tilt) or (3) eccentricity (non-circularity) of the orbit, we can use those parameters to define the shape of the constellation.

The spacecraft in row 5, column 5 of this 9×9 matrix is in the middle. Let’s say that this single spacecraft travels in a circular reference orbit. The others are orbiting at the same period, either ahead or behind the reference orbit, above or below it (in a north-south sense) or inside/outside of it (in an altitude sense). With the right combination of slightly perturbed, non-circular and/or inclined orbits, we can create a constellation that resembles our desired shape. Many spacecraft will be switching places once per orbit, some of the constellation seeming to rotate around a line from the center of the Earth to the reference orbit.

This dance is a straightforward consequence of the Clohessy-Wiltshire equations, which describe the motion of an orbiting body relative to a circular reference like the one we have here. The CW equations describe relative orbital motion, which we perceive as an interaction among spacecraft that happen to have the same orbital period, although in fact there is no gravitational attraction among these satellites that causes their motion.

CubeSat_tag

The figure above suggests a matrix of such CubeSats (larger than they would appear, given their relative spacing). Their attitude need not be particularly well-controlled as long as the LEDs emit a wide beam, and neither is their relative position. As shown, the 9×9 matrix is arbitrarily rotated and is displaying a symbol. Each needs to know its position in orbit so that the constellation, collectively, can produce the image that ground operators have sent it. That is, each one would illuminate its LEDs, or not, depending on its position and the time at which the constellation is supposed to create a certain image.

Flight software would make all this possible. A key ingredient is position knowledge, which would be available from GPS measurements. For example, at Cornell we built CUSat, a pair of satellites capable of detecting their absolute position in orbit to within a few meters. Their relative position would have been known to within a centimeter or so, had the flight computer not overheated and ended the mission prematurely. All that position detection took was a couple of homemade GPS boards, courtesy of the late Paul Kintner‘s lab, and some software conceived by Shan Mohiuddin, one of Professor Mark Psiaki’s students.

We’ll also need some propulsion. Options include electrodynamic tethers, cold-gas propulsion (prohibited by the CubeSat spec, for the most part), and electric propulsion. There are many forms of electric propulsion, but among those I am partial to solutions that involve ionic liquids for their power efficiency and scalability. Or, for a much lower-cost solution, Rodrigo Zeledon has figured out an innovative way to use water for propulsion: the ultimate cheap, green propellant, and compatible with the CubeSat spec.

Having a constellation that can illuminate part of the sky on command offers many interesting possibilities. Here are a few:

  • More is better. A much larger constellation—higher resolution—takes us from dot-matrix characters toward a jumbotron or video billboard in the sky.
  • The opportunities for art are legion. I’ll suggest only one. What if the constellation could behave in a way that seems to interact with the stars as it passes them? The constellation’s light might shudder, change color to blue, or twinkle as it passes an exoplanet. It might warm to the rising sun by changing color, or it might show a sequence of images that resemble Apollo’s chariot. In the case of higher resolution, maybe our formation responds to passage through an astronomical constellation by acting out some scene from Greek mythology.
  • A news crawl in the sky? There might be a business case for this concept.
  • Astronomy lessons: as the constellation passes a particular celestial object, seen from a specific region on the ground, it identifies the object and offers information about it. In fact, if we use the FITSAT trick of high-frequency modulation of the LEDs, we might be able to transmit simultaneously in different languages, asking only that the user look through binoculars with blinking apertures (like 3D shutter glasses for some home TVs), unique to his or her language.
  • A game in which people on the ground can aim a laser pointer at the constellation—not recommended when aircraft are present—with the goal of interacting with the light: turning on or off LEDs, or changing their color. The constellation would be a blank canvas, and we Earthlings could paint on the night sky.
  • Interaction like this raises the possibility of a game—maybe celestial 囲碁 (Go), requiring only two colors of LED, to be played in tag-team fashion by those who see the game board pass overhead.

I take the FITSAT existence proof to be enough to convince folks that a 1U CubeSat could be capable of certain aspects of this mission. Propulsion and additional power may require another 2U worth of spacecraft bus volume and mass. At $100K to launch these 3U CubeSats, it’s over $8M simply for the launch cost. Traditionally, one might double that cost as a very rough estimate that accounts for the space hardware. Include the resources for ground stations, and let’s guess a $20M investment is needed for a commercial enterprise that could tag the night sky with Earthlings’ celestial musings.

Follow the Light

chipsat_iss

On a hot day, we might say that the sun beats down on us. It’s literally the case: those photons carry momentum, despite that they’re massless. As they bounce off a surface, they impart momentum, i.e. they provide a propulsive force without propellant. Because of this force, mere light can accelerate a spacecraft to high speed. There’s your interplanetary spacecraft, right there—a solar sail. Here’s the spacecraft design question: what opportunities present themselves when we consider very small solar sails? Can we do better than the classic approach to the problem?

The idea of a solar sail has been around for quite a while. Arthur C. Clarke wrote “The Wind from the Sun,” a story about a solar-sailing regatta in which large, diaphanous spacecraft race one another with light propulsion. Small, meter-scale solar-sails have been launched, with modest success. The basic physics are not really in question. In fact, NASA is now building a 1200 m2 experimental solar sail to investigate the technology, the largest ever, known as Sunjammer. It’s an inexpensive demo of a very lightweight structure, including inflatable booms and other wonderful innovations from L.Garde, Inc.

Solar sails accelerate in proportion to the surface area that reflects solar photons, and in inverse proportion to the mass of the total space system: i.e., the larger the faster, and the heavier the slower. So, an ideal solar sail is super-thin, yet rigid. Dupont now makes a 0.1 micron-thick material that is suitable for solar sails. But the sheer dimensions of typical sails require an explicit effort to stiffen the structure, e.g. with booms (hence Sunjammer’s inflatable components). Some have proposed spinning a thin sail so that centripetal acceleration keeps the sail stretched outward. Spin also helps keep the attitude fixed in a convenient way. To be precise, let’s say that there’s a linear dimension, L, that characterizes the width or diameter of the sail. That area goes with L2. And let’s say that its mass, or volume, changes with L3. The acceleration changes with area per mass, or L2/L3=1/L. So, as L decreases, acceleration increases, all things being equal.

Of course, they’re not quite equal. There’s a lower limit on the thickness of the sail, and larger spacecraft can have disproportionately thin sails. But remember that the larger the sail, the more mass is devoted to keeping it stiff. That’s where a satellite-on-a-chip comes in. It’s an idea that we’ve been working on at Cornell since early 2005. We call them chipsats. We even made some prototypes, thanks to collaborations with Draper Lab and Sandia Labs. In fact, in a few weeks about 128 circuit-board prototype versions will launch and will be deployed. They’re called Sprites (the name given them by Dr. Justin Atchison) and will be launched on the Kickstarter-funded KickSat led by Zac Manchester. By early April, we may know how well this basic concept works.

One thing a chipsat does exceptionally well is that it remains stiff despite being very thin. A single silicon wafer (maybe 25 microns thick), about 1 cm square, might be enough to transmit very small amounts of data from space. Its tiny antennas are essentially rigid, too, despite being thinner than a human hair. But it’s a got a great “lightness number,” comparable to typical solar-sail designs. Think about it. If you shrink a spacecraft uniformly, so that the acceleration due to pressure effects changes with 1/L, that little chipsat has a big advantage. As L becomes small, that acceleration grows. So, a chipsat may be a perfectly adequate solar sail, without any of the complexity that larger solar sails bring.

We can do better than the Sun, at least this far away. We can concentrate the light that acts on a chipsat, maybe with a parabolic mirror. Or maybe with a laser. Sure, let’s use a laser. How much power we need depends on how much momentum we want to impart. More precisely, the photon pressure P, in Newtons per square meter (N/M2), is simply the power per area (e.g. in Watts per square meter) divided by the speed of light: P=E/c.

For example, if a 1 cm2 chipsat is fully face-on to a beam of light that covers its surface, the area is A=0.0001 m2. If it’s essentially solid silicon, whose density is 2330 kg/m3, its mass is m=0.000005825 kg, i.e. 5.825 mg. Let’s say m=6 mg. The acceleration would be a=F/m, where F=PA. So, P=ma/A and E=cma/A. The power W would be W=EA=cma.

To lift off from the surface of the Earth, this little thing would have to feel a force just a little greater than gravity, whose acceleration at Earth’s surface is about 9.81 m/s2. The laser power would need to be W = 300,000,000 x 0.000006 x 9.81 = 17,142 Watts.

The degree of unreasonableness of this estimate has to do with several issues. First, can you get a laser this powerful? Sure. Off-the-shelf industrial laser diodes are available at 10 kW. (The Army even put one on a truck as a weapon.) Doubling or tripling that number should be within the reach of current technology. How about the fact that the laser will be a little sloppy, or in any case it won’t exactly cover the 1 cm2 chip? OK, let’s gang together a half dozen of these diodes and point them upward in parallel, maybe with the help of an array of precisely steered mirrors. That’s less than six trucks worth of electronics, if we extrapolate from the Army’s design. What about the fact that directing nearly 20 kW worth of laser power would probably vaporize the little chipsat in an instant? Now that’s a good question.

The answer lies with the technology of dielectric mirrors. It turns out that reflecting off metal always incurs losses. The photon that reaches the surface of the metal induces a little electromagnetic response in the metal, which then releases a new photon. That process involves some loss of energy because of the unavoidable electrical resistance of the metal. A dielectric mirror literally reflects the same photons, with no such electromagnetic response (they can’t respond that way; they’re not electrical conductors). Dielectric mirrors reflect better than 99.999% of the incident light, but only in narrow bands. Well, conveniently, laser light has exactly one wavelength. That’s as narrow as it gets. This near-perfect reflection leaves only 0.17412 Watts behind, only about 70% more power than sunlight at Earth’s distance to the Sun. In short, I’d expect the chipsat to get less than twice as hot as if we just left it sitting out in the sun.

It’s also hard for this system to deal with Earth’s atmosphere. Wind gusts would blow the chip around, forcing it off the beam. (Dr. Leik Myrabo’s Lightcraft had a related problem during their White Sands tests, although the physics are entirely different from what I’m proposing here.) Setting aside atmospheric disturbances for a moment, let’s consider the problem of beam divergence, the tendency of the beam to spread out. It’s going to happen. And it happens in proportion to the wavelength. Say we use a 500 nm (green) laser. After a 1 cm narrowest point, which the laser folks call the “waist,” the beam diverges with an angle of 0.000016 radians. After 628 m, the beam has spread out to twice that thickness, so that its intensity is only a quarter of what it was when the beam was 1 cm wide. The beam becomes so weak that the initially high acceleration peters out, and the chipsat reaches only about 117 m/s. Maybe more important, the beam attenuates while the spacecraft is still close to the Earth. That is, the beam weakens faster than gravity does, which means that the chipsat falls back to Earth (in fact, it would hover at some distance above the ground, where gravity balances the photon pressure of the laser).

Two ways to address this problem. Assuming that only modest adjustments in wavelength are possible (so, we’ll assume they don’t help), we adjust the optics, widening the beam as much as possible. If it can be widened to 10 m, the photon acceleration drops slower than gravity. However, this approach is flawed because the intensity is much lower, and 1 g can’t be achieved to begin with.

The second way is to start in space (and now we don’t have to deal with the atmosphere), with a wide beam, say 10 m (a hundred-fold increase). Now the chipsat can accelerate for much longer, reaching 10 times that speed eventually. Another hundred-fold increase in beamwidth (not really possible) provides another factor of 10 increase in speed.

Increasing the beam width won’t get us what we want. It attenuates the power too much. To make the chipsat more effective, we have to change its lightness number, i.e its surface-area-to-mass ratio. Let’s add a skirt, a sort of tiny solar sail, made from that Dupont material, perhaps supported by the chipsat’s own 5 cm antennas, for a 28 cm square patch of thin material. With a density of about 1420 kg/m3, that patch adds only 0.11 mg, an increase so tiny that we can neglect it in the following calculations. And let’s set the beam width at the same number, 28 cm.

Now the chipsat accelerates to LEO escape velocity (11030 m/s) after about 3 hours’ laser firing. And we really don’t need a half dozen lasers after all. The diverging beam actually helps in that regard, bathing the chipsat in ever-widening laser light as it accelerates along the beam, despite whatever imprecision there may be.

So, that’s one way to create an interplanetary satellite-on-a-chip, using what amounts to current laser technology, if we can afford to launch such a laser into orbit and power it. Again, it should be about the size of a large truck, with a solar array not far from what NASA will be building for the asteroid rendezvous mission. But once you do, you can send an unlimited number of chipsats on interplanetary trajectories. And chip the light fantastic.

Lunar Xistera

xisterawithcrater

What if you could land on the Moon without a rocket motor—in fact, just by landing on a runway and rolling to a stop with more-or-less familiar mechanical brakes? And what if you could take off again without a rocket, simply by using an electric motor?

Yes, I’m aware that there is no air on the Moon, and only a few centimeters of what one might call atmosphere (and is in fact electrostatically levitated dust particles). I’m not proposing that an aircraft would lift off the surface with aerodynamic effects. I’m considering the possibility of a spacecraft that lands at orbital velocity and slows down from there. To take off again, the spacecraft must reach orbital velocity as it travels along this runway.

Why bother? Quite simply, a rocket takes a lot of fuel. For reference, each Apollo mission that landed on the Moon comprised both a lunar descent stage (10,149 kg) and an ascent stage (4,547 kg), for a total of 14,696 kg. About half of that total was propellant. In our example, let’s assume that we want to land 20,000 kg on the surface of the Moon. And why that number? It’s the low end of the total mass NASA calculates a human Mars mission needs to land on the surface of Mars. So, that total might make sense for a lunar landing as well—for instance, the case of a mission with a longer duration than any of the Apollo landings. For a spacecraft to be in orbit just above the surface of the Moon—assuming it’s at the average lunar radius of 1,740 km—it has to be traveling faster than 1,679 m/s. So, for it to stop by the end of the runway, it has to get rid of 1,679 m/s worth of energy. And for it to take off again, it has to attain that speed (or more). Unlike Apollo, our spacecraft may be able to use the same hardware—the wheels or something else mechanical—to land and take off. It does not necessarily expend propellant in the process. So, right there, I anticipate some significant mass savings. And this same vehicle can land and take off repeatedly, without refueling. Nice.

How long this runway would have to be involves some guesswork. Here are some of the numbers involved in my guesses. The FAA says that 1,829 m is sufficient for most aircraft under 90,718 kg. Longer runways exist, e.g. O’Hare’s runway 28, at 3,963 m. However, different issues are in play here, notably that gravity is lower on the Moon and likely doesn’t let the brakes decelerate the vehicle as quickly as they would on Earth without skidding. And the absence of atmosphere gives greater determinacy to the spacecraft’s touchdown, i.e. landing precisely at the beginning of the runway. So, I take it that the overrun area and other forms of margin are less necessary. Of course, most aircraft land at speeds far below that of our orbiting spacecraft. In fact, they land at speeds lower than that of the Space Shuttle, which used to land on Earth at 366 km/hr (104 m/s). Good automotive brakes can decelerate at about 1 g, and let’s assume that that principle holds for lunar gravity, where g=1.622 m/s2.

Decelerating at that rate from orbital velocity therefore requires at least an 869 km-long runway. That seems very long. Inconveniently, expensively long. Let’s try scaling up from those FAA guidelines, using the ratio of kinetic energy as a scale factor. For the same mass, that ratio is (1679/104)2=260.6. So, that basic runway distance would scale up to 477 km. Still quite long!

My dad, a former Marine Corps pilot, has a better answer, or I think he would if I were to ask him. Naval aviators extend a so-called tailhook from the back of their aircraft to snag a cable (one of several available attached to hydraulic cylinders) that slows down the aircraft over a relatively short distance: from 240.8 m/s to zero in about 104 m. Those are high gs, and I doubt it feels very nice. Nevertheless, at no more than 23,000 kg, those aircraft are about the mass of our spacecraft, albeit with about 1/50 of the spacecraft’s kinetic energy. So, how about a series of arresting gear, like those cables, over a distance of about 25 km? The spacecraft would decelerate at a withstandable 56.4 m/s2 (5.7 g, or 5.7 times Earth gravity), and it would take about 7.7 seconds. Quite a ride, but nothing the Navy hasn’t seen, and actually quite a bit more gentle than landing an aircraft at sea. But let’s add 20% margin to that length and call it 30 km.

Making a lunar runway requires something like concrete. We have an estimate of its length, but the volume of concrete depends on its thickness and width, too. Now, width seems not to be very important, judging by the lessons learned from aircraft carriers. Let’s say 10 m, which is more generous than what naval pilots require. As for thickness, we need enough concrete to prevent the landing from crushing the runway and to resist deformations of the Moon’s surface (yes, there are moonquakes). Our spacecraft is traveling a lot faster than an airliner, but its weight is far less—both because it has less mass and because the Moon’s gravity is only a sixth of Earth’s. While airport runways range between 25 cm and 1 m in thickness, I don’t see why ours needs to be any thicker than the most extreme terrestrial runway, at 1 m. Even that is probably excessive, but the point here is to come up with an upper limit of how much material is needed.

It certainly would take a lot of effort to bring concrete from Earth. And this runway requires 300,000 m3 of material. Naturally, we would build this runway from local materials—the lunar regolith. There are myriad recipes for lunar concrete, although the only solutions I’ve encountered require bringing quite a bit of material from Earth. So, here’s my recipe, which doesn’t:

Let’s begin by considering small rovers that can create regular, comparatively smooth bricks by sintering lunar material, as has been demonstrated at the Johnson Space Center (JSC) and elsewhere, or perhaps some other process. For sintering, the rovers will need solar panels and time, and an insulated (ceramic) mold that compacts the regolith (like WALL-E compacts trash), but not much else. And they can be at it for years as part of a robotic precursor mission before anyone is ready to land on the runway. Say each brick consists of a liter of material (10 cm on a side), with about 3.1 kg of mass each. There are 1,000 in a cubic meter and therefore 300 million bricks in this runway.

There’s a classic solution: melt regolith into bricks, whether with a 3D printer or some sort of oven and a mold. A 400 W rover could create a brick every eight hours—one hour during which it collects the material and later places it, and seven for heating up the sample (as in the JSC tests) from 350°K to 1,100°K. The bricks need to reach 1000°C for the silica to fuse, and although the JSC tests held it there for three hours, this slower heating would require less hold time. How much? I don’t know. This is just a ballpark figure. The specific heat of the regolith varies with temperature and was reported by some folks at Harvard to be about 1 J/g/degK at room temperature—i.e. 1,000 J/kg/degK in useful units. I modeled the specific-heat variation as linear, extrapolating from that Harvard data. This estimate is based on 1 m2 solar panels at 30% efficiency, for about 400 W of power during the 14 1/2 Earth-day-long lunar day. And I assume that about 20% of this available power is lost in electronics, imperfect insulation in the mold, et al. So, about three bricks per Earth day per rover—at least, while the sun is shining. Half the time it doesn’t shine, even on the Moon, simply because the Moon rotates as it orbits the Earth. (Incidentally, this sintering could all be done a lot faster with nuclear power, but I’d rather focus on a readily built system.) So, this approach would take 54,800 rovers 10 years to complete.

Forget that! Way too many rovers, obviously. I say fabricate the bricks out of frozen mud: regolith+water, which is far more brittle but could be repaired every time with far less effort than building a sintered-brick runway. With a supply of water, and in the cold, each brick would take maybe 5 minutes. And at that speed, we’d need only 570 rovers. That still seems like a lot of rovers, but at 50 kg each (the scale of the Violet spacecraft), that’s about 28,550 kg—one landing’s worth of rovers. Maybe plan for three landings, since we’ll need all that fuel etc. before the runway is built. Still, three landings and 10 years gets us permanent infrastructure for lunar transportation.

In preparation, a strip of the lunar surface is cleared of boulders. Also not hard for some small-scale rovers to achieve.

An adhesive mortars the bricks together. Again, proposed solutions for such mortar are legion. A particularly appealing one is the use of sulfur as a binder and as mortar, and that’s not hard to find on the Moon. That solution would also require no materials to be brought from Earth. However, if the mud bricks are solid enough to resemble terrestrial bricks, I would propose that we use water again as mortar—simply freeze the bricks in place, which is a solution that both uses in-situ material and also lends itself to straightforward repairs, as long as the ice is not exposed to the sunlight. So, protecting the surface of the mortar would be necessary, again using local material. Regolith itself—a thin layer of dust—might be enough. And this principle raises an important issue: sunlight would soften these bricks, turning them into mud. The simplest solution would be to land at night. Another, less simple, solution would be to build this runway in a permanently shadowed crater, of which there are several. The constant shadow ensures constant sub-freezing temperatures, which would keep the runway solid. In fact, these locations are also where water is found on the Moon’s surface. However, the location would be near a lunar pole, which may be limiting (although there are many reasons why a polar outpost could be a good idea, such as the availability of permanent sunlight and shadow).

After each landing, rovers inspect the runway. They seal cracked bricks and dribble water into the interstices as needed. Or they remove bricks entirely and replace them. Now for an interesting adaptation. What if the runway were not straight but, in fact, curved and banked—for example, along the edge of a crater. Some of the larger craters, like Tycho, are wider than 50 km. The tighter the radius and greater the bank angle of this runway, the higher the centripetal acceleration that would keep the spacecraft from skidding, thanks to increased friction at the wheels. So, how about a runway with an initial, flat landing region that curves into a lower, circular track? With no atmosphere, the Moon doesn’t require that the runway be entirely horizontal. The spacecraft’s initial approach simply allows the vehicle to begin tracking the runway’s kinematics, its path, which I suggest should be tilted so that the vehicle’s path is parallel to the lunar surface, but curved, like a jai alai xistera.

extrathickxistera

Let’s say the spacecraft decelerates at 5 g (Earth gravity, again), i.e. 49.05 m/s2. The force it feels would be inward, i.e. toward the runway surface, to keep the wheels in contact, as in the case of terrestrial runways. At this deceleration, the runway spirals inward over its roughly 28 km length, and there’s no need for the arresting device. This banked runway’s shape is a little harder to build than that of a flat runway, but it’s likely easier to operate, is a lot shorter than the alternative, and requires no hardware sent from Earth other than the rovers that build it. The image above is an exaggerated view of the runway: too thick and wide (I am showing it that way for clarity), but the curvature and other parameters are exactly what would accomplish this goal.

The runway merely needs to withstand 49.05 x 20,000 = 981,000 N inward, toward its surface as the spacecraft travels along the curve. It also has to withstand that same amount as a shear, along its surface, as the vehicle brakes. Even doubled (2,774,000 N), that force is far lower than commercial airliners apply to terrestrial runways.

Incidentally, for cargo only, a much higher g-load would be possible. Say 15 Gs. In that event, the spiral runway could be less than 10 km, as long as the runway could withstand the force.

Now, let’s free up our thinking even more. Do we really need those bricks? If landing in soft regolith—powdery sand—is possible, all that may be necessary would be for microrovers to clear the large rocks and boulders. The motivation for this banked spiral is to avoid a large number of bricks. So, one might return to the 800 km or longer runway, if it’s possible to find such a stretch of open, flat area on the Moon. A quick look at a lunar map suggests that it may be. Such a runway may be even shorter, given the drag of the regolith on the landing gear. The downside is that the drag of the regolith may be hard to predict and may overturn the landing vehicle.

So, in summary, we have several concepts here. There’s a long, flat 800 km runway that may have a sintered-brick surface or may simply be a soft, rock-free area. There’s a thoughtfully curved, banked runway that is much shorter—10-30 km. And there’s a 30 km runway with arresting gear, like on an aircraft carrier.

The spacecraft that lands on this runway needs wheels, or maybe skis. But if the goal is to take off again, a set of wheels makes more sense to me. Could they withstand the landing? A key issue is that the wheels must come in contact with the ground without too much relative velocity. Aircraft are able to land with wheels that spin up as they contact the runway, but the orbital speed is much higher. A 1 m radius wheel is not far from what large commercial aircraft use. Such a wheel, rotating at just over 16,000 RPM, would contact the runway without skidding. 16,000 RPM is fast, though. The tensile strength of the material must be quite high for the wheel not to tear itself apart at that speed, let alone the other forces associated with landing. A carbon-fiber composite wheel is necessary here.

Spinning up these wheels is not trivial. The International Space Station uses control-moment gyroscopes (CMGs) for attitude control, and their rotors require a long time to spin up—many hours. That’s because the spin motors typically are used only to keep the rotors spinning. On the rare occasion that a spin-up is necessary, they go as fast as they can. But that’s not very fast. So, I would anticipate that the wheels for this spacecraft need to begin spinning up many hours before landing. The power would come from solar energy, though, not propellant. A really useful feature of establishing that much angular momentum in the three-or-more wheels is that the spacecraft would have a high momentum bias, stiffening its attitude dynamics and allowing for a lower-risk approach to the runway, with little or no pitch or yaw motion. The landing gear need some sort of shock absorbers, like the oleo stroke gear on other aircraft. That’s a largely off-the-shelf component.

At this point I need to acknowledge that I’m not the first to consider all of these ideas. Some, perhaps, but not all. After reading the first draft of this post, a key member of my vast editorial staff introduced me to the work of Krafft Ehricke. Ehricke was a futurist and visionary technologist. He came up with the notion of a lunar runway long before I did, and lots of other great ideas besides. He had in mind several permutations, roughly along the lines of two of my three architectures: a long, dusty runway cleared of boulders and a paved surface. He put quite a bit of effort into the former, looking into the behavior of regolith for a vehicle that might land in it. But I have to say that his thinking, like mine, was driven by the spirit of his age. For him, a nuclear powered system to gather regolith and produce concrete was not much of a stretch. But for me, having seen how money is spent and how work is prioritized in Washington, I am focusing on a much leaner design that involves readily launched technologies with comparatively low cost. And, perhaps most important, I have benefited from recent discoveries, from Clementine to LCROSS, that confirm that the Moon is simply loaded with water. Ehricke had no idea. In fact, most of us assumed that the Moon was simply bone dry. Until about a decade ago, our exploration-mission architectures had humans bringing all the water they would ever need. That fundamental principle even shapes today’s architectures. It’s time for a re-think.

I claim that this banked and pitched, mud-brick runway built by robotic rovers in a permanently shadowed lunar crater is a new idea. It allows a spacecraft to land in a short distance, seems feasible to build on a useful time scale, and requires no fantastical technological breakthroughs.

Taking off again requires some more attention. I’ve given some hints at how it might be accomplished already. However, since this post is already quite long, and I’ve already offered about four new ideas here, I’ll save an analysis of this maneuver for a future post.