I understand ISS uses control moment gyros as the primary attitude control system. As the article states, CMGs eventually get "saturated", a state in which they can no longer absorb momentum. This can only be rectified with an external torque, from the onboard thrusters or the (significant) gravity gradient torque. How often does this need to be done on ISS, typically?
I did some more digging with this, and while I didn't find an explicit answer to my question, I did come across some interesting resources.
First, this paper states that they use reaction control jets to desaturate when the total momentum reaches 13000 ft-lbf-sec. However, there is no information about how long it takes for this amount to accumulate.
Second, this (fairly recent) presentation is very informative. It states that a "Torque Equilibrium Attitude" is used so the cumulative torque over one orbit is "approximately zero". So, as in the first paper, CMG torques will be (nominally) periodic.
Towards the end, a great chart of propellant mass vs. time (over a 3 month period) is shown. Excluding thruster tests and propellant transfers, I count four maneuvers, all during rendezvous/docking activities.
All of this leads me to conclude three things. One, the frequency with which this needs to happen is dependent on the docking schedule, as they impart significant non-periodic torques. Two, the nominal attitude is such that there is very little secular buildup in angular momentum. Three, the desaturation maneuvers with thrusters are not needed very often (e.g. daily), and in fact over a three month period, the only thruster firings occurred during docking activities. So, desaturation maneuvers not due to docking happen, at most, perhaps 3-4 times per year, and likely less.
Edit: I should also mention that there are quite a few journal publications from the 90s written about optimal control laws for the ISS. However, they were not open access, and an answer to this question (simulation-based or on-orbit) was not found in the abstract/first page.
Virtually all systems that do this use some sort of a continuous process. The typical process is something like this:
- A large change in momentum is required. The momentum change is handled by the reaction wheel. Reaction wheels basically work by changing the rotation of the spacecraft. You can think of it like standing in the center a roundabout and turning around in a circle. The roundabout will actually start turning the other direction. Reaction wheels have a maximum speed about which they can rotate, thus limiting their maximum limits of the absorbed momentum.
- The system dumps the momentum slowly in other forms. For most low earth orbiting spacecraft, they use magnetometers, which essentially re-orient the spacecraft using the magnetic field of the Earth. Other systems might include slight thruster maneuvers, or holding the momentum until the spacecraft needs to stop. Alternatively, small thrusters, often known as Reaction Control System (RCS) can be used. Typically, the reaction wheels try to bleed of momentum as quickly as they can, in a continuous fashion, if using passive means or magnetorquers, or they hold off as long as they possibly can and use an RCS sytem
The gravity gradient works basically because if you are rotating an object, the heaviest part tends to point towards the Earth. This is a completely passive system, which can work quite well.
The information that I have available indicates that the ISS does not use magnetorquers, but rather will store the momentum until it is so high that it must desaturate, when it accomplishes via the use of small thrusters. This is modeled quite accurately in Kerbal Space Program.
The goal then of the reaction wheels is to do two things.
- Sometimes the momentum is counteracted by the reverse direction after a small period of time.
- Minimize the number of times the RCS thrusters have to fire.
How often this happens isn't public knowledge, but I would speculate it is around a couple of times per day. However, as @Chris pointed out, there is a presentation that covers some of this information from NASA. Specifically, there's a few numbers that can be pulled out:
- The average amount of torque stored before a desaturate is around 14000 lb-ft/sec, or 18000 N.
- "Hundreds of kg/year of propellant" can be saved by reducing RCS use via clever algorithms.
- Assuming a thruster ISP of 300 (Slightly high), the fuel per wheel desaturate is approximately 60N, or 6 kg.
- To save "Hundreds of kg/year", and still using some fuel, let's estimate that the fuel usage for RCS/year is about 300 kg.
- Put all of that together, and there is roughly 50 desaturate maneuvers per year. I believe this estimate is somewhat low, I would expect 1-2 per week.