Could Magnetorquers be used on the ISS?

Question

The way that the ISS manages it's attitude now is to use a set of reaction wheels for primary control, and occasionally firing small thrusters to allow the wheels to despin themselves. This isn't always a practical response, as it uses fuel continually.

The way that many satellites manage to do this is with Magnetorquers, which align themselves with the Earths Magnetic Field, albeit in an active way.

What I want to know is,

• Under what conditions would the management of the Space Station be too difficult using only Magnetorquers?
• Could only Magnetorquers be used to control it, and if only some of the time, when would the most difficult times to use them arise?

Answer 1

In addition to Undo's answer, I'll try to give a "zeroth order", back of the envelope analysis for this:

First, from my answer here, we have $$T=DB=2DM/R^3$$ where $T$ is the torque applied by the torquer, $M$ is the magnetic moment of the Earth (about $7.96\times 10^{15}~\text{tesla}\cdot \text{m}^3$), $D$ is the dipole induced by your torquer, and $R$ is the distance from the center of Earth's dipole.

Now, mechanics tells us that $$T=I\alpha$$ where $I$ is the moment of inertia and $\alpha$ is angular acceleration. We'll take $I_{xx}=127908568~\text{kg}\cdot\text{m}^2$ from here for our purposes, and let's say you want to impart a modest angular rate of $0.05~^{\circ}/\text{sec}^2\approx 0.0009~\text{radians}/\text{sec}^2$.

So, the magnetic dipole required in this case would be $$D=\frac{I\alpha R^3}{2M}=\frac{127908568\cdot 0.0009\cdot (6478*1000)^3}{2\cdot 7.96\times 10^{15}}\approx 1.966\times 10^9~\text{A}\cdot \text{m}^2$$

This is a massive dipole. If we calculate the dipole moment of a wrapped coil with $N$ turns as $A\times I\times N$, and even assume a fairly massive 1 meter cross sectional area, and a generous 10 Amps of current, a torquer using 1 mil copper wire would be 1 meter long and have a layer of copper 13 cm thick. This would weigh about 1200 kg, which is pretty damn heavy. Consider this with Undo's more qualitative points, and it's starting to look like a bad idea, even if it's not physically impossible.

Answer 2

I can't give a definitive answer until I have numbers on how much torque that the devices can output, which I wasn't able to find on the Interwebs.

However, Wikipedia paints a grim picture for the possiblity of their use on larger sattelites:

Disadvantages

The main disadvantage of magnetorquers is that very high magnetic flux densities would be needed if large craft had to be turned very fast. This would either necessitate very high current in the coils, or much higher ambient flux densities than are available in Earth orbit. Subsequently, the torques provided are very limited and only serve to accelerate or decelerate the change in a spacecraft's attitude by minute amounts. Over time active control can produce very fast spinning even here, but for accurate attitude control and stabilization the torques provided often aren't enough.

A broader disadvantage is the dependence on Earth's magnetic field strength, making this approach unsuitable for deep space missions, and also more suitable for low Earth orbits as opposed to higher ones like the geosynchronous. The dependence on the highly variable intensity of Earth's magnetic field is also problematic because then the attitude control problem becomes highly nonlinear. It is also impossible to control attitude in all three axes even if the full three coils are used, since the torque can be generated only perpendicular to the Earth's magnetic field vector.

Any spinning satellite made of a conductive material will lose rotational momentum in Earth's magnetic field due to generation of eddy currents in its body and the corresponding braking force proportional to its spin rate. Aerodynamic friction losses can also play a part. This means that the magnetorquer will have to be continuously operated, and at a power level which is enough to counter the resistive forces present. This is not always possible within the energy constraints of the vessel.

It's not a definitive 'no', but it certainly seems unlikely that the power requirements to keep such a large satellite as the ISS aligned in a certain way would be cheaper than the amount of propellent used to align the craft currently.