Another "Spinning the ship for artificial gravity" thread

[peadar1987]

Your window of opportunity is almost as big as you want to make it. First, we agree that we can set up a pass at an almost arbitrary distance from the station to have ship at rest at closest approach, right? There is question of precision, but we aren't trying to grab a dumb cargo drone with a station. We don't need it to pass within inches or even meters of the station. If you can give me +/- 50m, I'd shoot for a 100m approach and it'd be fine. Rest can be covered under power. Ideally, you need to go from free-fall to accelerating at 1g precisely as you pass under the station, at which point you are hovering and the rest of approach is trivial. Realistically, you can't do that, but you don't need to, either. What you do is start throttling up a few seconds in advance, which will bring up the line of closest approach closer to the station, curving in your trajectory. So long as you watch the time to closest approach, closest approach distance, and your velocity relative to the station, it's a pretty straight forward maneuver with a window in tens of seconds at 1G.

I'm sure that what you were working on required a perfect approach precision and an instant transition from inertial to accelerated movement. This is not the case with a ship being flown by an experienced pilot. It's just not the same problem.

But you know what? I'm prepared to bring it down to a simulation. I have a VTOL simulation I've written a while ago. With a few modifications, I can get it to simulate something space-worthy. All I have to do is get rid of all of the aerodynamics code, modify thrusters a bit, change the control scheme, and add a bit more info on the HUD. Oh, and I'd have to model and simulate a simple station, I guess. That will require a few extra bits of collision code, but it's no trouble.

What I need from you are parameters you are willing to accept. Specifically, with what precision you would allow me to measure my velocity and position relative to the station? I'd also take accelerometer data and combine it with tracking data via Kalman filter. So I need error on acceleration data as well. And what about the Shuttle? For simplicity, lets say maximum linear and angular accelerations you'd allow. Naturally, I need something in excess of 1G along the vertical axis. Everything else will be pretty gentle, but I'm worried if I just make up numbers you'll accuse me of rigging it.

As for the station, lets say 40 RPH as mentioned earlier? That would put the station's diameter at about 4km to provide 1G at the outer edge. That's a nice big target to aim for. I can do either a wheel-type station or a tether. Your call.

Yeah, our system was for boosting a 500kg payload from earth to lunar orbit, so it was to have, as a best case scenario, an accuracy of +-100m. If you're interested, I can try and dig up some of the graphs and data and stick them in another thread.

You're suggesting that you match velocity with a point on the surface of the station, and then provide centripetal force by thrusting inwards? That's probably a far better idea for something that has the fuel budget and thrust to do that. The brief for mine was to be something as passive as possible, so I was kind of working off the same assumptions for this as I was before.

I'm happy enough to take your word for it on the numbers. I don't have the knowledge of dynamics and control that would be required to actually give you decent numbers to plug in.

[PTNLemay]

Basically, any station large enough for you to be landing a shuttle on, you won't be needing to worry about Coriolis effect.

But the tangential speed is going to go up as the space station gets large, not down. The angular velocity is what drops as you scale your space station up. What this means is that as you make your station larger your "rotations per minute" will drop, but the "rim speed" that the inhabitants (or ships docking along the outer wall) experience will increase. That's one of the reasons why we can't make space stations infinitely large using regular modern building materials. If we tried to build a ring world or something like Halo using simple steele, the speeds involved in spinning it up would rip the station apart.

Here are a few numbers I got from a spin-calc. This is for simulating 1.0 G of acceleration.

As your space station starts to get large enough, the speeds you have to match get pretty high. It would be like trying to land a 747 on a giant train. A train that's following a huge curving arc. Yes, you can burn the engines to push towards the center axis of the station to try and follow the arc, but it's not going to be as simple as hovering over the surface of the Earth. In fact, if the ship is coming at the station from the outside it would feel more like a helicopter coming to "land" itself on the bottom part of a bridge (plus all the speeding and arcing I mentioned earlier). From the station's perspective, you're coming up at them from their downwards direction (starwards).

Though, having said all that... apparently Babylon 5 is ~800 meters across (radius of 420 m). So it's outer rim will be spinning at "only" 64 m/s.

EDIT:

For comparison the top speed of an aircraft carrier is ~80 knots, or only 42 m/s. And I'm guessing they try to stand as still as possible when they have jets landing on them.

Edited December 7, 2013 by PTNLemay

[Dweller_Benthos]

Very nice discussion, and more than I originally bargained for, thanks everyone.

So, on to a few more interesting thoughts. I presume this one has been worked out, but the air inside the station, wouldn't it twist itself into a giant tornado centered along the axis of the station? Would the friction of the air next to the ground speed it up more than the air in each successive layer towards the center? Thus creating a swirling vortex in the middle? Or is there not enough of a difference in a station even 5 miles in diameter to make much of an effect? I suppose some sort of system of fans would be installed to counteract any ill effects of the air not all spinning at the same rate. Not to mention all of the air wanting to settle towards the bottom.

Also, is flight in the station effected in any way? Taking off in some sort of helicopter or VTOL ship from the ground gives you a lot of momentum in the direction the station is spinning, let's presume the air near the ground is also moving at near the same speed and that there isn't significant shear in the air as you move upwards that would make control of the ship impossible. Once you've left the ground, if you fly anti-spinwards, would you effectively negate the "gravity" and go into free fall, or would you have to apply continuous thrust/power?

[PTNLemay]

@ Dweller

I think people would like a bit of turbulence because it would kind of simulate weather patterns. If only to a limited degree. Having a bit of wind blowing on your face every now and then is something you'd miss if you lived in space too long, I imagine.

I do think flying could work, the tangential velocity problems are really a thing when you're dealing with a vacuum, but I suspect the air in the habitat would definitely help curb some of the coriolis effect. After a while the air will be spinning along with the rest of the station. It's like if you put a cup of water on a rotating plate, eventually the water in the cup will be spinning almost as fast as the cup, no?

They might even design some of the buildings along the inside of the strucutre in such a way to encourage the air to keep flowing along with the motion of the station. Like big fins that keep the air stirring away at the same speed. Unless this produces too much turbulence in the higher levels of the habitat... truthfully I don't know enough about complex fluid mechanics to know what would happen, at least not in any serious detail.

[PakledHostage]

As your space station starts to get large enough, the speeds you have to match get pretty high. It would be like trying to land a 747 on a giant train. A train that's following a huge curving arc.

Though, having said all that... apparently Babylon 5 is ~800 meters across (radius of 420 m). So it's outer rim will be spinning at "only" 64 m/s.

Let's do a thought experiment... Consider a very hypothetical object the size of Babylon 5 that has a surface gravity of 2g's and that rotates at the same rate as Babylon 5. The "gravity" experienced by someone standing on the equator at the surface of this object would be 1g. How would you land on that surface? How would it be different than lading on a more realistic airless celestial body? How would the control be different than what K^2 is describing? I think you'll find that the control requirements for landing on all of these examples are the same, only their magnitude and direction differ.

EDIT:

For comparison the top speed of an aircraft carrier is ~80 knots, or only 42 m/s. And I'm guessing they try to stand as still as possible when they have jets landing on them.

It is too bad that MrShifty has been away from these conversations for a while now. He'd be able to answer your questions about aircraft carrier ops. You'd probably be surprised to find out that it is the opposite. The best I can offer you to support this is to suggest that you read about Doolitle's raiders in WWII. They launched bombers off a carrier by steaming full power into the strongest winds they could afford to tolerate and wait for.

Edited December 7, 2013 by PakledHostage

[K^2]

But the tangential speed is going to go up as the space station gets large, not down. The angular velocity is what drops as you scale your space station up. What this means is that as you make your station larger your "rotations per minute" will drop, but the "rim speed" that the inhabitants (or ships docking along the outer wall) experience will increase. That's one of the reasons why we can't make space stations infinitely large using regular modern building materials. If we tried to build a ring world or something like Halo using simple steele, the speeds involved in spinning it up would rip the station apart.

Have you done docking in KSP? That's done at over 2km/s. Have you had difficulties with these colossal speeds? Or did you find that only the relative speeds matter? Because it should have been the later.

Coriolis effect is proportional to angular velocity. So is every other problem you are likely to encounter. The larger the station, the easier it is to land on using conventional VTOL techniques.

Now for structural stress, it's actually pretty simple. Station rotates at a uniform angular velocity. So we can consider it from a co-rotating frame, in which the only source of structural stress is the centrifugal force. Centrifugal force is proportional to ɲr. Because É is constant throughout, it just increases linearly from center starting at 0G and growing to 1G at the rim. What this means is that you are basically building a suspension structure. Making one that's several km in diameter is an engineering challenge. But it's well within the structural strength of modern building materials.

I'm happy enough to take your word for it on the numbers. I don't have the knowledge of dynamics and control that would be required to actually give you decent numbers to plug in.

Alright. I've gotten basic handling in "Earth's Gravity" sorted, so I'm just going to keep the current parameters. Going to start building the station now.

[peadar1987]

Now for structural stress, it's actually pretty simple. Station rotates at a uniform angular velocity. So we can consider it from a co-rotating frame, in which the only source of structural stress is the centrifugal force. Centrifugal force is proportional to ɲr. Because É is constant throughout, it just increases linearly from center starting at 0G and growing to 1G at the rim. What this means is that you are basically building a suspension structure. Making one that's several km in diameter is an engineering challenge. But it's well within the structural strength of modern building materials.

I think the main problem wouldn't be with centrifugal force, it would be with the force from a pressurised interior. Unless you had whatever space colony or whatever laid out as interconnected pressurised modules on the inside surface of the ring, I suppose.

[K^2]

I would definitely go with modules for reasons of not only structural integrity, but also safety. However, keep in mind that if I take two rectangular rooms, each one pressurized, and put them together so that they share a wall, then by taking out the wall, the only thing I lose is the tension support the wall provided. Stress on all other walls remains exactly the same. Which means I can replace a wall with some pillars. Taking this to the bigger structure, I can have fairly large open spaces, so long as I'm willing to tolerate an endoskeleton of supporting frames.

The downside is that the mass of the station will scale with volume, rather than surface area. But that's a well known problem with pressurized containers.

[PTNLemay]

Sorry about the comment about the structural stress, I threw it in as an after-thought but I realize it's not related to the proper discussion and could only lead to derailing. We can debate it further in an other thread.

Have you done docking in KSP? That's done at over 2km/s. Have you had difficulties with these colossal speeds? Or did you find that only the relative speeds matter? Because it should have been the later.

I agree, but in a Kerbin orbit the two objects that need to rendez-vous are travelling in near parallel paths. Yes there is a curve to those orbits that is similar to how a ship would have to match the curvature of a spinning space station, but in a proper orbit that curve is planet-sized, whereas in a space station the curve is a few kilometers across at the most. Plus there's no gravity to continuously tug you towards the center of rotation, you need engines or some fancy grappling hook to keep push/pulling you towards the station.

That's all I'm saying, that it can be done, but that it would be more difficult than usual docking or landing due to the continually shifting heading. The spin rate for the Babylon 5 example is 1.47 rotations per minute. That's one rotation every 41 seconds. I imagine it would take more than 41 seconds to secure the ship to the outer wall (unless it involved those super grappling-hooks or a giant net like was mentioned earlier). Hell, in just 20 seconds the target will have done half a rotation, and is now moving in the opposite direction to the ship's initial heading. The ship would have to perform drastic changes in it's trajectory to keep up.

[K^2]

The difference between docking to a rotating and non-rotating station is precisely by the accelerated frame of reference. And as we've discussed, that's the same problem that a VTOL aircraft has to deal with. There is no significant difference between fighting gravity and trying to match rotation with a rotating space station, so long as station is large. And something on the order of B5 or larger is definitely large enough.

It's not the most fuel-efficient way to dock. I would probably need close to two minutes under full thrust to do the docking, so we are talking over 1km/s of dV reserve. But in terms of difficulty of flying approach, it's really not that bad as I intend to fully demonstrate.

[LLlAMnYP]

This may have been already considered or dismissed, but why not just dock to a structure at the axis of rotation of the station?

[PTNLemay]

@ LLiamn

Oh yes we know that, it would be safer to do it that way. The reason we're on this line of questioning is that Dweller asked "what would it be like for a person slipping down from the center of the axis to the inner edge of the cylinder." And a comparison was made to doing the opposite, moving from the outside and coming towards the central axis and the spinning outer wall of the station.

Then me and K^2 started fixating on one specific aspect of the discussion (namely how safe that would be) ignoring all the other questions. As internet arguments tend to do.

[LLlAMnYP]

Yeah, the comparison with VTOL craft is nice, but they do generally use air-breathing engines, right? 1000 m/s "spare" dV in space and on earth are two entirely different things.

Naturally, a person moving from the center of rotation to the outer edge of our spinning construction would experience quite a sizeable Coriolis effect.

Ah! My bad, this has already been mentioned.

Now that I think of it, Dweller also wondered about the motion of air in such a construction. Now wouldn't that be very similar to the motion of free electrons in thermal equilibrium in a solid under a uniform magnetic field directed along the axis of rotation?

Edited December 8, 2013 by LLlAMnYP
I will always read the entire thread, I will always read the entire thread...

[PTNLemay]

I was wrong about that, actually. K^2 was right. Coriolis effect has to do with the sensation that things are falling sideways in a spinning frame of reference, and it does diminish as the station gets bigger. That's why we have a very week coriolis effect on the surface of the Earth even though we're moving at hundreds of meters per second (sideways).

To use the analogy I did earlier matching the sideways motion is like landing on an aircraft carrier. So long as the carrier and the aircraft (spacecraft) are moving at the same speed, it's not that hard. The actual problem lies in the vector change. That is, in what direction you are heading in space (to stretch the analogy it's like if the aircraft carrier was bobbing up and down on huge waves). The smaller the space station, the more quickly you need to spin to provide gravity. That means in relatively short amount of time the spot you're trying to land on will have moved 90 degrees relative to your heading. So you need to secure yourself to the outer wall of the station fast.

I made this sketch of a design I think would help. You fly in through the gap as you get close, and quickly nudge yourself sideways. Then you do like K^2 was saying, and treat it like you're hovering over the surface of a regular planet. And ease yourself down on to the deck.

Edited December 8, 2013 by PTNLemay

[LLlAMnYP]

Yeah, that's quite clear. Coriolis would be noticeable if you were to dock at the rotational axis and then move radially all the way to the outer edge of you station. If the docking bay is small relative to the diameter of your structure, Coriolis effects would also be negligible. The tougher part would be to match velocities with the docking port (which puts you on a very different trajectory compared to the station as a whole) and then as soon as you are aligned with the docking port you need to start accelerating towards the center of the station at 1g just to appear to be stationary in the co-rotating frame of reference.

[PakledHostage]

The tougher part would be to match velocities with the docking port (which puts you on a very different trajectory compared to the station as a whole) and then as soon as you are aligned with the docking port you need to start accelerating towards the center of the station at 1g just to appear to be stationary in the co-rotating frame of reference.

But this takes us back to the point that K^2 made earlier, and which I tried to highlight in my post yesterday. Doing that isn't really any different than landing on a celestial body, only the direction of the thrust control inputs is reversed. Consider the landing of Apollo 12 adjacent to Surveyor 3. They flew an unpowered trajectory to the landing zone and then started the lander's engines to hover to a landing within hopping distance of the robotic probe. The landing required several km/s of delta-V and a great degree of precision to achieve, yet they pulled it off.

Obviously, landing on the central axis of the rotating spacecraft would be easier and cost less delta-V, but I don't think landing on the outer surface of a sufficiently large rotating space station would be a show stopper.

[LLlAMnYP]

Sure! The difference is that for a VTOL aircraft the velocity that matters is relative to the atmosphere which is normally more or less matched with the landing pad (exception - strong, but intermittent or frequently changing winds), whereas in space the trajectory of a spacecraft going at the same speed as the docking port at a given moment may deviate from the trajectory of the docking port itself quite rapidly even if the space station is truly huge.

In fact, while the rpms of a large station may be quite small and you'll be able not to worry about the docking port turning away by 90 or so degrees while you're struggling to get yourself in an "orbit" around the station, the actual velocity of the docking port relative to the rotational axis is comparably larger and that leads to a bigger difference in the orbit of the approaching spacecraft as compared to the orbit of the station.

[K^2]

There is no such thing as absolute velocity. How fast something is moving is absolutely irrelevant. In station's frame of reference, the docking port is static.

What matters is how the target is accelerating. And docking port is accelerating radially at precisely 1G. Exactly the same as any point on the surface of our planet.

Yes, in case of VTOL aircraft, atmosphere can make things easier. Or a lot harder if there is cross-wind. But that's why PakledHostage mentioned Apollo 12. They were operating in identical conditions. They had to match velocity of the surface and then land on it while matching the Moon's surface gravity. There is no difference here.