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.
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.
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.