### With 3 Reaction Wheels, the Universe is Ours

"The more torque I can come up with, the better" - Tim Lincecum

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My formal training in physics may be limited, but I still remember learning about the law of conservation of angular momentum way back in high school. Now don't worry, it's not that hard! If you're familiar with conservation of linear momentum:

p = mv
(momentum = mass * velocity)

Well then angular momentum is basically the same thing, it's given by the formula:

L = Iω
(angular momentum = moment of inertia * angular speed)

Yikes, weird variables! But I promise they're equivalent - moment of inertia for angular momentum is akin to mass for linear momentum, the only difference being that moment of inertia is a factor of both the mass and radius of rotation of the spinning body. The example they always gave in school was that of a spinning figure skater: she starts of with her body extended and spinning slowly, but as she draws her limbs in (reducing her radius of rotation, and therefore her moment of inertia), her spinning increases because angular speed must go up to conserve angular momentum!

The equivalency extends to changes in linear / angular momentum too. If you want to change the linear momentum of a moving object, you can apply a force (F). If you want to change the angular momentum of a spinning object, you can apply a torque (τ). And just as Newton's 3rd law states that for every action there is an equal and opposite reaction, that same principle applies to torque!

Now I learned the concept of torque through a way cooler example than a silly figure skater in a textbook: younger Hans spent a lot of his childhood watching nerdy TV documentaries, and the Discovery Channel used to have a really awesome show called Weaponology that explained the history and development of modern weaponry. In the episode about the attack helicopter, early helicopter prototypes suffered from an annoying problem: the act of generating lift by spinning the rotor blades one direction (adding torque) created an equal and opposite reaction... meaning the body of the helicopter would spin in the opposite direction, obviously destabilizing the vehicle! The solution: add a single, small tail rotor that rotates perpendicular to the main rotor to cancel out the torque!

 I'm honestly astonished I still remember this episode, it came out 15 years ago!It's actually on YouTube, skip to 5:57 for where they discuss the torque problem

Great, now that we're past the long intro: what does this have to do with space? There's a mechanism commonly used on spacecraft called a reaction wheel. It applies the law of conservation of angular momentum - the same one that was a nuisance for the helicopter - to maintain very precise attitude control in orbit. The spacecraft provides an electric power source (usually from solar panels) that spins the reaction wheel. As it speeds up, the law of conservation of angular momentum causes the spacecraft to counterrotate. With three reaction wheels - one for each axis of motion - you can point a spacecraft anywhere and maintain its orientation... no heavy thrusters and no fuel required! Quite useful for a space telescope that needs to point very steadily at a star lightyears away

 This is a sweet demonstration of how reaction wheels maintain the cube's orientation, even as the surface is tilted

So reaction wheels are pretty sweet, but what are their drawbacks? First, reaction wheels are only able to rotate the spacecraft around its center of gravity, they're not capable of translational force. So if you have to actually move your spacecraft from A to B, then you need an actual thruster

Second, reaction wheels are susceptible to failure; in fact, many high profile spacecraft ended their missions after multiple reaction wheels failed. Two of Hubble reaction wheels have failed before, though fortunately they were replaced during the various crewed servicing missions. Most famously, the Kepler exoplanet-hunting telescope launched in 2009, but after just 4 years, two of the four reaction wheels had already failed! One of the four was there for redundancy, but with the loss of the second wheel, Kepler could no longer maintain 3-axis control. Mission planners were able to compensate using an ingenious method that balanced Kepler against pressure from the solar wind, but the telescope's operations were still hampered and Kepler needed to occasionally burn its onboard propellant to maintain orientation. When the propellant ran out in 2018, Kepler had to be retired

 Just like how you can balance a pencil on your fingertip, the solar wind became the third reaction wheel on Kepler!

Finally, the last drawback of reaction wheels is that they can become "saturated". The torques from the reaction wheels are not the only torques acting upon the spacecraft. Over time, the spacecraft must also overcome external torques like atmospheric drag, gravitational perturbations, or even tiny vents or leaks on the spacecraft. Let's say a spacecraft has been in operation for 5 years already, and its x-axis reaction wheel is currently spinning at 5,999 RPM to maintain orientation, but it has a design limit of 6,000 RPM. This means that over the past 5 years, the spacecraft has already transferred a lot of torque to this reaction wheel in order to maintain attitude control. At this point, if the onboard computer determines that the spacecraft needs to correct for even more torque in the x-direction, the only option is for the spacecraft to use some other mechanism - like burning propellant with its thrusters - to "null out" the stored angular momentum. It can't just slow down the reaction wheel, because the act of slowing down the wheel is applying a torque, and that torque will apply a counter-torque that will destabilize the spacecraft

 All it takes is three wheels to point anywhere in the Universe!