Attitude Control Gyroscopes on Spaceships

[DaveC426913]

I'm not looking for fiction; I'm looking for physics.

Assumptions:
- An engine efficient enough that you can afford to thrust for very long periods - maybe fusion? (OK, that's fiction)
- A lot of maneuvering (eg. you could thrust until turnaround point and then decelerate)
- With a lot of maneuvering and a single main engine it would be would be better to rotate the ship with gyros rather than retros.

What would the properties of the gyro(s) need to be?

Does it need to be at the centre of mass?
Can you have more than one?
Can multiple gyros be away from the centre of mass?
Clearly, the more spherical the ship, the better use it could make of the momentum, so an ideal ship might be as spherical as practical. (just a supposition)
Is there a ratio of how large and how fast the gyro must be to turn the ship efficiently?
Would the gyro spin down quickly under all that applied torque? (You could always bleed off some thrust to power a generator that would keep it spun up.)

 

[FactChecker]

This can get you started: https://en.wikipedia.org/wiki/Control_moment_gyroscope

 

[DaveC426913]

Fascinating. Thank you! That answers several of my questions - and raises a few more.
I assume current gyros, such as those on the ISS provide a gradual, gentle rotation. I'm imagining a spaceship that can/needs to turn fast, like to do evasive maneuvers (which is why I envision a nearly spherical ship a la ballet pirouette analogy).

The reason I wanted to understand if the gyro(s) need to be at the CoM, is because it would be better to put the pilot there, so that vertigo is minimized when under max rotation.

How big a gyro - as a ratio of ship mass - would one need, to spin the ship, say, 90 degrees in one second? Obviously that depends on how much momentum the gyro could store (which be limited in top speed, because of materials). I guess such a set of gyros (sound like you'd need at least 4) would take up a fair chunk of ship's volume/mass.

 

[jbriggs444]

The reason I wanted to understand if the gyro(s) need to be at the CoM, is because it would be better to put the pilot there, so that vertigo is minimized when under max rotation.

Why should it matter where the gyros are? The ship rotates around the center of mass regardless of where the gyros are placed.

 

[FactChecker]

I assume current gyros, such as those on the ISS provide a gradual, gentle rotation. I'm imagining a spaceship that can/needs to turn fast, like to do evasive maneuvers (which is why I envision a nearly spherical ship a la ballet pirouette analogy).

I doubt that gyros will help in evasive maneuvering in outer space. They will rotate but not redirect motion. So the spaceship will just wiggle around without evading anything. It's not like an airplane, where rolling redirects the lift force vector and changes the direction of motion. Now, if you are talking about turning the ship to point a rocket nozzle or a gun, that is something gyros might help with. But there are probably better ways to accomplish that. During significant maneuvering, gyros have the problem of reduced control authority due to saturation.

 

[mfb]

If you want fast changes in thrust direction, rotate your engine, not the whole spacecraft . Rotating the whole spacecraft structure by 90 degrees in one second is unfeasible for any realistic spacecraft large enough for humans. I don't see any scenario where this would be useful either.

Back of the envelope estimate: Dragon 2 has a dry mass of 6.5 tons, CST-100 Starliner seems to have a bit more but it is hard to find numbers, Orion will have a dry mass of 9.3 tons. These are basically the minimal viable capsules to support humans in space for a week, or a smaller crew for a few weeks if absolutely necessary. They don't have a big engine. Let's say your spacecraft has a mass of 10 tons (excluding gyros) at typically 2 meters away from the center of mass for a given axis of rotation. That gives it a moment of inertia of 40,000 kg m². For full three axis control, you need three gyros. Let's make them huge at 1 ton each as ring with 4 meter diameter (basically filling a whole wall of the capsule). That gives them 4,000 kg m², or 1/12 of the remaining spacecraft which is now at 48,000 kg m² if we rotate one gyro and the other two are dead mass.

The minimal torque approach for a 90 degree = pi/2 spacecraft rotation in one second is a constant angular acceleration of 2pi/s² for half a second and deceleration of the same amount afterwards. That needs a torque of 48,000 kg m² * 2pi/s² = 300,000 Nm, a peak differential angular velocity of 13 pi/s and a peak power of 12 MW. Going from 0 to 12 MW in half a second, then from 12 MW to -12 MW in "zero time" and back to 0 in half a second will need a really unrealistic motor, a huge battery array and various other oversized components. You would probably need most of the spacecraft mass just for motors and powering infrastructure.

Making your spacecraft larger just makes it worse. Scaling up all masses by a constant factor is fine, but scaling up the size makes the required torque and power increase with the square of the length, with nothing to compensate it.

 

[DaveC426913]

I doubt that gyros will help in evasive maneuvering in outer space. They will rotate but not redirect motion.

Which is why you have the main engine burning continuously.

during significant maneuvering, gyros have the problem of reduced control authority due to saturation.

Yeah, I read about saturation. Fascinating. It's why you'd need at least 4 gyros, like the ISS has. That side-steps the saturation problem:(https://en.wikipedia.org/wiki/Control_moment_gyroscope#International_Space_Station)

 

[DaveC426913]

If you want fast changes in thrust direction, rotate your engine, not the whole spacecraft .

Rotating the engine while thrusting doesn't in-and-of-itself move the craft from its trajectory. Mostly what it does is spin the craft. You still have to return the engine back to straight so that the thrust is now oblique to the initial trajectory. Then you can move off-course.

Whereas, if you rotate the whole craft, you accomplish both steps in one, because the thrust is aligned with the CoM so it immediately contributes to oblique acceleration.

OK, I guess I'm getting a bit hair-splitting now in terms of usefulness of the idea. Considering what you wrote below, I can see the benefits of gyro-rotation disappearing before my eyes:

Rotating the whole spacecraft structure by 90 degrees in one second is unfeasible for any realistic spacecraft large enough for humans. I don't see any scenario where this would be useful either.

Back of the envelope estimate: Dragon 2 has a dry mass of 6.5 tons, CST-100 Starliner seems to have a bit more but it is hard to find numbers, Orion will have a dry mass of 9.3 tons. These are basically the minimal viable capsules to support humans in space for a week, or a smaller crew for a few weeks if absolutely necessary. They don't have a big engine. Let's say your spacecraft has a mass of 10 tons (excluding gyros) at typically 2 meters away from the center of mass for a given axis of rotation. That gives it a moment of inertia of 40,000 kg m². For full three axis control, you need three gyros. Let's make them huge at 1 ton each as ring with 4 meter diameter (basically filling a whole wall of the capsule). That gives them 4,000 kg m², or 1/12 of the remaining spacecraft which is now at 48,000 kg m² if we rotate one gyro and the other two are dead mass.

The minimal torque approach for a 90 degree = pi/2 spacecraft rotation in one second is a constant angular acceleration of 2pi/s² for half a second and deceleration of the same amount afterwards. That needs a torque of 48,000 kg m² * 2pi/s² = 300,000 Nm, a peak differential angular velocity of 13 pi/s and a peak power of 12 MW. Going from 0 to 12 MW in half a second, then from 12 MW to -12 MW in "zero time" and back to 0 in half a second will need a really unrealistic motor, a huge battery array and various other oversized components. You would probably need most of the spacecraft mass just for motors and powering infrastructure.

Making your spacecraft larger just makes it worse. Scaling up all masses by a constant factor is fine, but scaling up the size makes the required torque and power increase with the square of the length, with nothing to compensate it.

 

[DaveC426913]

Why should it matter where the gyros are? The ship rotates around the center of mass regardless of where the gyros are placed.

Yes. That's what I wanted to determine. I wasn't sure if placing the gyro(s) off-centre from the CoM would affect their usefulness at these kinds of power. It'd be fine for a slow rotation, but I was thinking a high rotation might essentially waste some of their angular momentum, as well as place undue lateral stress on components.

 

[jbriggs444]

Yes. That's what I wanted to determine. I wasn't sure if placing the gyro(s) off-centre from the CoM would affect their usefulness at these kinds of power. It'd be fine for a slow rotation, but I was thinking a high rotation might essentially waste some of their angular momentum, as well as place undue lateral stress on components.

To the extent that the gyros are more dense than the rest of the ship, moving them away from the center of gravity will tend to increase the moment of inertia of the vessel. The angular momentum delivered is fixed regardless.

 

[FactChecker]

Which is why you have the main engine burning continuously.

Sorry. Right. I forgot about that from your original post.

Yeah, I read about saturation. Fascinating. It's why you'd need at least 4 gyros, like the ISS has. That side-steps the saturation problem:(https://en.wikipedia.org/wiki/Control_moment_gyroscope#International_Space_Station)

I don't know how that works. I don't think it side-steps the problem. The article says that the ISS uses its high gravity-gradient torque to desaturate the CMGs. That may take a long time. I am not sure how well the small, mild maneuvers of the ISS would compare with "evasive" maneuvers.

 

[mfb]

Rotating the engine while thrusting doesn't in-and-of-itself move the craft from its trajectory. Mostly what it does is spin the craft.

It does both. For the center of mass motion it doesn't matter where your engine is, only the thrust direction matters. If you rotate the engine at its current location (instead of rotating it around the spacecraft , what I was imagining) then the engine won't be able to keep firing in the same direction quickly based on the rotation of the spacecraft , but that is a different issue.

 

[DaveC426913]

Sorry. Right. I forgot about that from your original post.I don't know how that works. I don't think it side-steps the problem. The article says that the ISS uses its high gravity-gradient torque to desaturate the CMGs. That may take a long time. I am not sure how well the small, mild maneuvers of the ISS would compare with "evasive" maneuvers.

Extrapolating further into the realm of fictional tactics, I guess what you might do is "burn" all your ... uh ... 1/saturation ... in the emergency evasion, then you'd have to desatch them once the danger has passed.

 

[Filip Larsen]

If you are talking about evasive manoeuvrers (i.e. change of trajectory) then I assume fairly high thrust acceleration is available. If so, then there should also be a fair bit of torque available to change orientation via "traditional" thrust vectoring and it may be useful for you to relate performance of CMG with that.

If the spacecraft already can accelerate linearly with acceleration $a$ and has moment of inertia $I = k m r^2$ for some value of $k$ then via thrust vectoring I get (on my supply of envelope backsides) that the spacecraft also has access to a maximum angular acceleration of $$\dot{\omega}_m = \frac{a}{k r}.$$ This can be compared to the required average angular acceleration $\dot{\omega}_r$ needed to change the orientation of the spacecraft through the angle $\Delta\psi$ in the time $\Delta t$ of $$\dot{\omega}_r = 4\frac{\Delta\psi}{\Delta t^2}.$$

For instance, to change orientation 90 degree in 1 second of a spacecraft with $k = \frac{1}{2}$ then it needs $\dot{\omega} \approx 2\pi$ which for a 3 g thrust is possible up until around 9 m radius. For a 10 g thrust that would increase maximum radius to around 30 m.

[Edit: corrected wrong power for radius r. I blame the poor state of my envelope backsides.]

 

[x_engineer]

In terms of evasive maneuvers, you would do better with a ship that blows itself apart with the pieces still connected by ropes, and then reassembles by pulling on the ropes.

Niket Patwardhan

 

[DaveC426913]

In terms of evasive maneuvers, you would do better with a ship that blows itself apart with the pieces still connected by ropes, and then reassembles by pulling on the ropes.

You;re supposed to add a after a post like that.

 

[happyhacker]

Was interested in the bit above about rotating the engine to spin the craft. If for example there were three engines in the 'rear' of the craft to provide thrust and only one of the outside engines was thrusting would that spin the craft. I'm more thinking of moving in the direction of travel in 'free' space rather than in orbit.

 

[Bandersnatch]

If for example there were three engines in the 'rear' of the craft to provide thrust and only one of the outside engines was thrusting would that spin the craft

Yes, it would. But it would also move forward. So it'd go in circles rather than just spin.

 

[x_engineer]

You;re supposed to add a after a post like that.

But also serious. Rotation of the ship is a completely ineffective evasive maneuver. If you are being targeted by some kind of missile (or ray), in space your center of mass trajectory is highly predictable and hard to change. But separating the ship into pieces is easier, and a missile (or ray) would go for the center of mass which would be empty of content. The only challenge is to get the pieces back together after the evasive maneuver, ergo the rope. At least three pieces, so there is not even a rope at the center of mass.

 

[DaveC426913]

Heh. Larry Niven did something like that in Protector. Not to avoid a missile (though he was being chased) but to use the tidal forces of a black hole as an escape.

Pak ships are comprised of three pods (engine, supplies, crew) strung out along cables like a pearl necklace. Going around a BH would have scattered the pods across the system. By disassembling them (manually), they passed individually around the BH and he simply gathered them up again afterward, while his enemies (in a similar ship) chased all around the system gathering their ship back together.