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.

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