Controlling a spacecraft is a little bit different than controlling an earthly vehicle, mainly because outside earth’s atmosphere there’s not much to push off. But aerospace engineers have some ingenious ways to get rockets and satellites where they’re going. You may have seen the yo-yo trick called "Around the World", but you probably didn’t know that spacecraft that actually do go around the world have their own yo-yo trick.
How do you keep a rocket or a satellite pointed in the right direction? You might think this is pretty simple: put an engine on the side you want to go away from right? But actually in the real world of space-faring vehicles it’s a little bit more complicated than that. Any time you apply a force that is not in line with the center of rotation, that’s called a torque. When you use a wrench, you’re torquing a bolt by applying a force offset from the axis of rotation. A torque is a product of angular acceleration, so any time you apply one, you’re going to induce some rotation unless there’s a reaction to compensate.
Naturally, we want to keep our spacecraft on the straight and narrow, but there’s so many torques that can influence its rotation. You can have aerodynamic forces, like strong winds or atmospheric drag. You can have perturbations from variations in gravity, effects from earth’s magnetic field, or even solar radiation pressure. You can also have internal torques from the spacecraft itself. If you’ve got an engine, maybe it’s not mounted perfectly in line with the center of mass. If you’ve got more than one engine, maybe one is a little bit stronger than the others. There’s a host of torques that can induce rotation of your spacecraft, so engineers have come up with a host of ways to counteract these torques and keep things headed in the right direction.
You can use control surfaces to react against the air rushing past the rocket just like an airplane. You can gimbal your engine to give you more control over the direction of thrust. You can use small directional thrusters located off-axis on your spacecraft, and you can also use flywheels to counter-rotate against any extraneous torques. All of these methods have their own advantages and disadvantages, but the overarching problem with all of them is that they’re complicated.
Now you may think that aeronautical engineers eschew the KISS principle. After all, "rocket science" is the ubiquitous analogy for something that’s overly complex. But consider this: If it’s a moving part or it creates incredibly hot and fast moving exhaust gases, there’s a chance that it might break, and if it breaks, there’s not a lot of opportunity to get a technician into the upper atmosphere or low earth orbit for maintenance or repairs. So attitude control engineers developed a dead simple, widely-used technique of attitude control called spin stabilization, and you can probably guess how this works.
If you’ve ever played with a gyroscope, you know that it resists changes in direction of its main axis. There’s a great Veritasium video if you want more details on the physics behind this. It works the same way with a rocket or satellite. If you spin the spacecraft around the axis it’s moving along, it will resist small torques just like a gyroscope. As an added benefit, if there is some asymmetry in the spacecraft, instead of accumulating torque in a single direction, now you’re averaging the asymmetry out around the main axis. This is a really simple method of stabilization, because it usually doesn’t require any additional moving parts or systems. But it does have it’s own disadvantage, namely that your spacecraft is wildly spinning in circles at the end of it. Now sometimes that’s okay, but a lot of the times, your instruments or sensors or cameras don’t work if they’re spinning so after your engine burn you want to despin. Naturally, there are several ways of dealing with this as well, but remember, we’re trying to keep things simple.
Let’s talk just for a minute on what it actually takes to despin something. A spinning body has a certain amount of angular momentum which is a product of two values: angular velocity (that’s just the rate of rotation) and moment of inertia which is a measure of how a body’s mass is distributed around its axis of rotation. A rotating rod has a low moment of inertia because its mass is concentrated around the axis. A rotating tube has a high moment of inertia because the majority of its mass is far away from the axis. Angular momentum is conserved as long as there’s no outside forces applied; that’s just Newton’s third law. So the angular velocity or spin rate is on a see-saw with moment of inertia. If one goes up the other goes down, and vice versa. This is really cool, because it says that even without any outside forces, there’s a way to reduce the speed of our spinning spacecraft: just increase the moment of inertia.
The classic example of this is the figure skater, and you can try this yourself even if you don’t skate. Spin yourself in an office chair with a couple of weights in your hands. If you bring in your arms, you decrease your moment of inertia, so your speed goes up to compensate. The yoyo despin works in exactly the same way but in reverse, except at the end you get your arms cut off. If you deploy small masses attached to cords wound around the satellite, just like a yoyo, as they unwind they increase the moment inertia of the system, decreasing the angular velocity. You can actually transfer all of the angular momentum into the masses, then release the cords, completely despinning the spacecraft.
I put together a model to illustrate this concept. First I turned a disk of MDF on the lathe and mounted on an aluminum tube with some bearings so it can spin freely. I’ve got a servo on top which is attached to a couple of quick release mechanisms. When the servo activates, it pulls these cords which release whatever is attached. There are two tethers with a fishing weights on each one, and these get wrapped around the disk and clipped into each quick release. This is powered by an Arduino, so I can push a button and activate the servo to release the yoyo masses.
When the yoyo masses are released, they start to unwind, increasing the moment of inertia of the system. Once they reach the end of their tethers, they slingshot forward, absorbing the rest of the kinetic energy before they’re released. The crucial parameters when you’re designing something like this are the length of the tethers and mass of the two weights. And actually if going for a complete despin, the initial angular velocity doesn’t matter, which is convenient because I could just spin the model by hand without worrying about how fast it was going.
I designed this to release the masses when they’re exactly radial, but it’s pretty tough to get this perfect, so sometimes the model was actually spinning in the opposite direction when the masses let go. In real spacecraft they have cool release mechanisms like explosive bolts, but I was not able to get my hands on these. And as cool of a demo as this is, it probably wouldn’t be much good for a science fair or career day unless you come up with a way to contain the flying masses. This is a problem in real spacecraft as well, and these masses can contribute to the ever-increasing amount of space junk orbiting the earth. But despite that, the yoyo despin is a really clever application of simple physics to accomplish an important job, and especially with spacecraft, sometimes simple is best.
Resources for Learning More
- These lecture notes have the basic equations for designing a yo-yo de-spin system.
- Orbital Mechanics for Engineering Students by Howard Curtis - This is the textbook I relied upon for design of my model.