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Maths and spaceships...

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knasser knasser's picture
Maths and spaceships...
I'm putting together my first Eclipse Phase adventure. I'm trying to be accurate and would appreciate some advice. I have a space station with a spinning ring. This motion creates a force of 1G on the inside of the ring angled outward, thus you have a habitable area. Now this I know is something proposed by scientists and appears in hard science-fiction, so is plausible. In trying to work out the actual numbers, I got the following: Using the formula: Force = mass * radius * (angular velocity)^2 I worked out 9.8N = 1kg * 800m * (angular velocity)^2 angular velocity = 0.111 radians/s. That is to say that at about 1.6km diameter (approx. 1mile), the station is doing a full rotation about once every 56seconds meaning with a circumference of around 5km, its outer surface is moving at a aroun 90m/s (approx 325km/h or 202mph) relative to a hypothetically stationary bystander. So there are two parts to this question. Is the maths right (which I think it is) and if so, how do you dock? Certainly you can come along the side and even match a velocity in one direction, but not an angular velocity. Now you could have a platform in the centre that was going in the opposite direction, thus effectively stationary in comparison. And a ship or a crew could land on that. You still ahve the issue of how to get from the central platform to the outer ring though. I suppose at the very centre, an angular velocity of 0.111 radians per second means less. You could concievably make a step from a (relative terms) stationary platform onto a spoke, following it outwards and facing the increasing weight as you climb your way toward the outer circle. (By the time you reached the outer circle you would be climbing "down" of course). But the smaller the platform the harder it is to land a ship on it and the larger the platform the more you get a jump when going from it to a moving spoke. You could have gradiated platforms in the middle. One stationary (in relative terms), this is surrounded by another ring that moves more, followed by a third ring, etc. That changes it from a single jump to a series of jumps. But I don't think that would work as the further you get from the hub, the larger the relative difference in speed is for the same change in angular velocity. You could start on the outside and work your way in. In this model, the torus has prongs sticking out of it that a ship could attach to. From there, you essentially climb your way up out of a higher G until you reach the lightness of 1G at the torus itself. Note that to avoid simply encountering an even more extreme problem of how you match angular velocity with the torus than you did when you were docking directly on the ring, these prongs need not be rigid. I'm thinking they're more like tethers that you could temporarily introduce some slack into by means of firing a retro-rocket at the end of one and then attaching the ship, enabling it slowly get winched in, picking up a matching velocity. There are a few downsides to this though. The first is that these tethers would probably have to be pretty long and the winching in process very slow. The second is that any ships wishing to dock would have to have appropriate equipment and structural integrity. The third is that ships with sufficient momentum may upset the orbit of the station itself. Naturally ships could use their own engines to assist in reducing their momentum once tethered which would be good. But all in all, it seems problematic. There's a fourth option which is that docking ships should match the spin of the torus itself as they dock. I presume that this means docking could be a fairly drawn out process as you wouldn't want to make large adjustments very rapidly to avoid stress on your ship and vomit in your cockpit. Also, if you want multiple ships docking, you have a problem as if the ships aren't docking in the absolute centre of your station, you have the angular velocity problem again. I suppose it's possible that you could have ships moved from the docking position once to a kind of holding area. You'd have to be very careful leaving if you didn't leave from the same central position as you could run the risk of part of the station smacking into you once you cast off. So you'd be best off having your ship returned to the central docking part before leaving. Yay! Spaceship queues! Right - thoughts and suggestions, please! :) K.
"We're here to save the planet. But not for free."
remade remade's picture
Re: Maths and spaceships...
About docking - if rotating station is sum of shapes O and X, then you can easily dock in the middle of X - first you match normal movement of station (hang over rotating landing pad), then match rotational movement of station and then you dock. Matching rotation of station could be performed by station itself catching the ship with some elastic cables and putting it in the dock automatically.
Zophiel Zophiel's picture
Re: Maths and spaceships...
Or the docking hub could be dead center. The ship's AI works with the station's AI to match rotation about the ship's center axis and moves into the docking hub. Once there it is locked to a platform and drawn up one of the spindles (or wherever).
Sir_Psycho Sir_Psycho's picture
Re: Maths and spaceships...
I'm not in any position to give you hard sci-fi advice, especially on maths. I was imagining this the other day, and in my head I went with docking on the outside of the ring. I chose this because there's more surface area on the outside of the hab for more ships to dock, which is one draw. Another reason is because once you're attached, the gravity inside your ship matches the gravity of the habitat, allowing you to "climb up" straight into the ring. I assumed it would be done with magnets to draw you in and ship thrusters and an AI pilot system stabilising the docking. Although I really like the idea of elastics proposed. Giant myomeric rubber bands? Excellent.
OneTrikPony OneTrikPony's picture
Re: Maths and spaceships...
Your math is corect. Here's an online calculator http://www.calctool.org/CALC/phys/newtonian/centrifugal There are a couple of pretty serious engineering issues here. Allow me to restate them. 1). how do you physicaly dock a ship to a rotating platform. -a). with out causing castostrophic sheer forces on a ship that's built as lightly as possible. -b). without using massive amounts of manuvering fuel to match the motion of the ship to the platform. (again in a ship that is built as lightly as possible.) 2). how do you transfer items with mass across the "gravity threshold" from the ship to the platform. -a). given that in all but one scenario everything transfered from the ship to the platform will experience the sheer force of the platform's 'gravity' in at least one axis. Getting across the "Gravity threshold" wether it's a habitat or a planetary body will always be a pain in the ass. At least as long as we cling to our silly affection for anthropomorphic forms. I believe the answers are low G habitats and small, powerful shuttles. I think that we can eliminate the configuration of the ship itself as a solution to the problem. Interplanetary freighters will probably allways be a stack of crew/cargo, on top of fuel, ontop of thruster in a realatively thin and long shape. This is the best way to optimalize the structure to cargo ratio. So usually we'll have a primary airlock at one end and thrusters at the other. Given the Thrust capabilities in the book. the only way for a ship powered by fusion rockets to physicaly dock with a rotating station would be to nose in to an airlock at the gravitational zero point (the center of the hub) of the station. This is pretty efficient from the standpoint of fuel costs and structural reinforcement. The ship needs only match the RPM of the station around its long axis then connect to the airlock. This works well for the ship but only alows two ships to be docked at the same time regardless of the size of the station. Somehow connecting to the outside of a station with Mars or greater gravity is well beyond the thrust capabilities of any ship not powered by metalic hydrogen engines. Therefor a fast shuttle is required. I like the idea of "tractor cables" but the sheer forces on the ship seem like they might be insurmounable on any ship that has managed to push itself across 150,000km of space in 24 hours. The Sum of my opinions (completely unsuported by arithmetic) the only safe place to dock a big ship is at the center of the stations rotation. And this could only be accomplished by matching the longitudinal rotation of the ship to the station. Interplanetary ships do not have the inate thrust capability to match the angular momentum of any station with more than micro gravity. using tractors or tugs to make a big ship match the angular momentum of a rotating station would likely tear that ship appart. A small shuttle powered by metalic hydrogen rockets would have all of the Delta-V necessary to dock with an airlock anywhere on a station with less than 3G's of angular momentum. (Bring your vomit bag!) Once a shuttle is docked shifting cargo is a simple matter of deviseing elevators of the apropriate type. (again bring your vomit bag.)

Mea Culpa: My mode of speech can make others feel uninvited to argue or participate. This is the EXACT opposite of what I intend when I post.