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Currently, science knows of precious few methods of simulating gravity on a spacecraft. These boil down to: using acceleration by thrusting the ship, spinning the ship (or sections of the ship) to utilize "centrifugal force", or placing a large mass under the ship (generally by landing on a planet). Centrifugal force is the method of choice for obvious reasons.
How fast will the ship have to spin in order to provide acceptable gravity?
Ca = 0.011 * Cr2 * Cl
Cl = Ca / (0.011 * Cr2)
Cr = sqrt( Ca / (0.011 * Cl))
- Ca = centrifugal artificial gravity acceleration at point X (m/s2)
- Cl = distance from point X to the center of rotation (m)
- Cr = rotation rate at point X (rotations per minute)
Remember that 1.0 g is 9.81 m/s2. Notice that as point X is moved further from the center of rotation the artificial gravity increases.
Instead of doing the math yourself, you can cheat and use SpinCalc.
"Soup's on," announced Lopez. "This is your messroom. Lunch in a few minutes."
Behind Lopez, secured firmly to the far wall, were mess tables and benches. The table tops faced Matt -- under him, over him, or across from him -- what you will. It seemed an impractical arrangement. "I'm not very hungry," one youngster said faintly.
"You ought to be," Lopez answered reasonably. "It's been five hours or more since you had breakfast. We're on the same time schedule here as Hayworth Hall, zone plus eight, Terra. Why aren't you hungry?"
"Uh, I don't know, sir. I'm just not."
Lopez grinned and suddenly looked as young as his charges. "I was just pulling your leg, kiddo. The chief engineer will have some spin on us in no time, as soon as we break loose from the Bolivar. Then you can sit down on your soft, round fanny and console your tender stomach in peace. You'll have an appetite. In the meantime, take it easy."
Two more squads filtered in. While they waited Matt said to Lopez, "How fast will the ship spin, sir?"
"We'll build up to one gravity at the outer skin. Takes about two hours to do it, but we'll eat as soon as we're heavy enough for you groundhogs to swallow your soup without choking."
"But how fast is that, sir?"
"Can you do simple arithmetic?"
"Why, yes, sir."
"Then do it. The Randolph is two hundred feet through and we spin on her main axis. The square of the rim speed divided by her radius -- what's the rpm?"
Matt got a faraway look on his face. Lopez said, "Come, now, Mr. Dodson -- pretend you're heading for the surface and about to crash. What's the answer?"
"Uh-I'm afraid I can't do it in my head, sir."
Lopez looked around. "All right -- who's got the answer?" No one spoke up. Lopez shook his head mournfully. "And you laddies expect to learn to astrogate! Better by far you should have gone to cow colleges. Never mind -- it works out to about five and four-tenths revolutions per minute. That gives one full gravity for the benefit of the women and children. Then it's cut down day by day, until a month from now we're in free fall again. That gives you time to get used to it -- or else."
Ed note: 200 foot diameter = 61 meters diameter. 61 / 2 = 30.5 meter radius. 1 g = 9.81 meters per second.
- Cr = sqrt( Ca / (0.011 * Cl))
- Cr = sqrt( 9.81 / (0.011 * 30.5))
- Cr = sqrt( 9.81 / 0.3355)
- Cr = sqrt( 29.24)
- Cr = 5.4 minutes
Someone said, "Gee, it must take a lot of power."
Lopez answered, "Are you kidding? It's done by electric-braking the main axis flywheels. The shaft has field coils wound on it; you cut it in as a generator and let the reaction between the wheel and the ship put a spin on the ship. You store the juice. Then when you want to take the spin off, you use the juice to drive it as a motor and you are back where you started, free for nothing, except for minor losses. Savvy?"
"Er, I guess so, sir."
"Look it up in the ship's library, sketch the hook-up, and show it to me after supper."
As it turns out, there are limits on the rotation rate. The Coriolis effect can induce nausea. 1 RPM is safe, at 3 RPM most can acclimatize but some cannot (and it takes some time for those who can), at 5 RPM a few can acclimatize but most cannot, and nobody can acclimatize to 10 RPM and above. The only way to increase gravity without increasing the RPMs is to increase Cl.
Or maybe not. Troy Campbell pointed out a recent study with some hopeful conclusions:
However, the data on artificial gravity is a bit out of date. The original research into it had subjects sick at 3 RPM and incapacitated at 6 RPM+. However, more recent research suggests that, by using incremental increases in rotation and making a few limb movements, adaptation can occur with almost no feelings of nausea. The old research (done on about 30 subjects) simply went from zero to full rotation. Moreover, the adaptation can be simultaneous with non- rotational adaptation. So, moving in and out of the rotating habitat for maintenance or whatever is no problem. It's thought that rotation rates of up 7.5 to 10 RPM are possible. This makes Discovery's 5.5m radius centrifuge a real possibility. In fact, with 10 RPM, you could crank it up to a handsome 0.61 G, or 0.34G if you want to play it safe at 7.5RPM.
There are some ship designs where the ship separates into two sections connected by cables and spun, in a desperate attempt to increase Cl. Please note that such a spacecraft is "spinning like a bola," not "spinning like a bolo."
The most common arrangement are ships that spin on their long axis, that is, the thrust axis. There is no common term for this, but "top" will do (as in "spin like a top"). Spin gravity is at ninety degrees to thrust gravity.
A variant on the "top" is the "centrifuge". This is where only part of the ship is spun for gravity while the rest stays stationary. Usually it takes the form of a large spinning ring with its axis coincident with the thrust axis (i.e., it looks like a pencil stuck through a doughnut). But there are some types where the centrifuge is internal, e.g., the Discovery from 2001.
Guido Lißmann had a few comments on the additional headaches that centrifuges give ship designers. They mostly center on the problem of "conservation of angular momentum":
If a spaceship has a spinning section to provide simulated gravity, and lest the whole ship is intended to spin, that section would need to be set in motion somehow.
If it is done by reaction engines, the connection between the non-spinning part of the ship and the spinning section would need to be literally free of any friction, otherwise, that part of the ship would eventually begin to spin also, and slow down the spinning section. Or another set of reaction engines would be needed to keep it from spinning.
But what I find more problematic is the above mentioned conservation of momentum. In a vessel with a spinning section set in motion by mechanical means or even contact-less linear electric motors strung around the circumference of the non-spinning section and the hub of the spinning section, the non-spinning section would obviously instantly spin once the spinning section is fired up, only in the opposite direction.
There would need to be a counter-rotating flywheel to counter this, spinning in the opposite direction of the main spinning section, or even a complete second spinning section turning the opposite way. Since a spinning section would need to be large not just to provide adequate room but also to have the necessary diameter to not necessitate a very high frequency of revolution, a flywheel would have to be substantial, and unless it has a double use, such as a radiation shield or the like, would be just a big lump of dead weight. Logically, a second habitable spinning-section would be preferable. Of course, a constantly burning reaction engine might be used, much in the same way as the tail-rotor of a helicopter, but that would just be a massive waste of fuel.
Also, there is the question of sealing the non-spinning section, like on the Discovery from 2001. Shaft-seals and the like would have to be huge lest the only way to get from the spinning section to the non-spinning section be so small as to necessitate contortionist-midget-astronauts. Huge seals are problematic, creating huge friction and needing to be kept clean. Labyrinth seals would be friction-less but not airtight (bad in a spaceship, unless one wants to include the entire spinning-section in the pressurised area of the ship). One could, of course, create to separate habitable environments for the two sections of the ship, but that would entail suiting up and cycling through two airlocks every time one has to rush from ones bunk to the control room.
The Problem With Hexagons
This clever design solves the problem of how to quickly assemble a wheel space station, with one tiny little drawback. You see, there is a reason that wheel space stations are shaped like, well, wheels and not like hexagons.
The amount of centrifugal gravity experienced is determined by the distance from the axis of rotation (the greater the distance, the stronger the gravity). So if you want the amount of gravity to be the same, the station has to be a circle.
Now, look at the below-left image. The segment labeled "SPACE STATION RIGID MODULE" is one of the hexagonal sides. The green lines lead to the axis of rotation (i.e., that is the direction of "up". Note the little dark men figures, they feel like they are standing upright). And the red lines are lines of equal gravity. You will note that they do not align with the module.
In the module, centrifugal gravity will be weakest at the center of the module, and strongest at the ends where it joins with the neighbor modules. Even though the module is straight, the gravity will feel like it is a hill. If you place a marble on the deck in the center, it will roll "downhill" to one of the edges.
As you see, the designers tried to compensate for this by angling the decks, but it really doesn't work very well.
Details can be found in Self-deploying space station final report .
In Heinlein's The Rolling Stones, some spacecraft are classified as "tumbling pigeons". They rotate end over end to provide artificial gravity (i.e., they spin on the short axis instead of the long axis). The idea is to increase Cl, that is, if you spin on the long axis Cl is the relatively tiny width of the ship, while if you spin on the short axis Cl is the length of the ship.
Of course, this means that in all the crew spaces in the "top" of the ship, the floor will become the ceiling ("top" is defined as the half of the ship that does not contain the engines, with the dividing line along the axis of rotation). In the novel, such ships were generally limited to passenger liners for tourists with weak stomachs.
Now, one would think that such a centrifuge would act as a titanic gyroscope, doing its best to prevent the ship from changing its orientation. Aerospace Engineer Bill Kuelbs Jr points out that if the centrifuge is a sufficiently large percentage of the ship's total mass, it will not prevent turning. What it will do is alter the axis of any turning force by ninety degrees. Rev up a toy gyroscope and try to turn it to see what I mean.
The solution is fairly simple. The turning thrusters will have to be effectively at ninety degrees to where you'd expect. In reality, this means that when the centrifuge is spinning, the "pitch the nose downward" control button will actually fire the "yaw to the left" thruster. An alternative solutions is to have two centrifuges that are spinning in opposite directions.
Another minor problem is load balancing. The spinning ship or centrifuge will have to make sure its mass is evenly balanced around the circumference, or it will start acting like an unbalanced clothes washer on spin cycle. Without load balancing, the simple act of the crew walking around could be a disaster. Load balancing could be accomplished by a series of ballast tanks and a network of pipes to pump water from one tank to another.
Yet another minor problem is the Coriolis effect. A thrown ball or other object will have its trajectory bend to the side, as if being blown by a cross-wind.
Which Way Is Down?
But the main design problem is that as a general rule the direction of "down" while under thrust is not the same as the direction of "down" while under spin gravity. The brute force solution is to force the crew to detach all the furniture from the floors that are now walls and put them on the walls that are now floors whenever the spacecraft changes mode. This is quite a chore. And there will be further problems with floor and wall mounted control consoles and related items. The alternative is rotating the entire room on gimbals.
In Space Angel (1962), illustrated by the legendary Alex Toth, the pilot's chair and attached controls rotate on gimbals independently of the ship. Of course there is no need to rotate the chair on gimbals since the Star Duster never ever lands on its belly like an aircraft, but the unsophisticated audience demands it.
Two Orientations, One Layout
Below is a crude but clever arrangement. Under thrust, "down" is in the direction of the red arrows and the green chairs feel like they are prone. When thrust is off, the ship is spun on its long axis for centrifugal gravity so "down" becomes in the direction of the yellow arrows. The green chairs abruptly feel like they are upright, and the crew can walk on the blue "floor". In other words, they deal with the problem by making the layout usable under either orientation. Due to the small diameter of the spacecraft, it will have to spin exceedingly fast to produce appreciable gravity.
|Level 6||10.16 m||0.447 m/s||0.05g|
|Level 5||12.70 m||0.559 m/s||0.06g|
|Level 4||15.24 m||0.671 m/s||0.07g|
|Level 3||17.78 m||0.782 m/s||0.08g|
|Level 2||20.32 m||0.894 m/s||0.09g|
|Level 1||22.86 m||1.006 m/s||0.10g|
Another possibility is an arrangement like the Pilgrim Observer. This is a variant on rotating the room on gimbals, it is actually a "gimbaled centrifuge". The three living quarters are held parallel to the spacecraft's long axis when under acceleration. At other times, they are extended at ninety degrees, and spun like blades of a propeller to act as a centrifuge. The direction of "down" is always the same, whether under thrust or spin. This also allows the hub to remain stationary, providing a mounting for all the telescopes and other sensors which would otherwise have to cope with being spun around. Not to mention simplifying the docking of small craft. In the diagram, the three living quarters arms and the thin ring they are attached to are the only parts of the spacecraft that spin, the rest of the spacecraft is stationary.
The blades can be spun up by attitude jets, or by a flywheel. The advantage of a flywheel is that the blades can be stopped by stopping the flywheel.
In the picture of the Pilgrim Observer, it looks like there are six levels on each blade. Use the distance from the floor to the center of rotation as "point X" in order to calculate the artificial gravity for each level. The Pilgrim spins at a rate of 2 revolutions per minute, the maximum radius at the bottom of the blade is 22.86 meters (75 feet), each deck is 2.54 meters tall (100 inches).
Dream Pod 9
The innovative people at Dream Pod 9 have an elegant version of the gimbaled centrifuge. Their ships have a centrifuge ring which pierces the centers of a series of rectangular habitat modules. The habitat modules can pivot on their axis. There are two habitats visible in the image above. In the head-on view to the right, they are at one o'clock and seven o'clock, with the pivot located where they intersect the ring. As in the Pilgrim, they pivot so that down is aft when the ship is under thrust, then pivot so that down is sideways while the ring starts rotating.
The pivot is the weak point, obviously. The pivots on the US Air Force B-1 bomber are only rated for about three gravities of acceleration.
Graham Baxter points out that the diagram pictured to the right makes more sense if the labels for "In Flight" and "In Free Fall" are swapped.
It strikes me that the design featured has the angle of the habitat modules backwards; instead of having the modules in a vertical 'office building' layout as shown, wouldn't it be better to lay them out horizontally, with the decks running parallel to the long axis of the module? With the decks laid out in this fashion, the module would have far less variation in centripetal force between decks when under rotation and depending on how the module was locked into place during acceleration, more/stronger anchoring points to the rotating frame as well?
At the very least, you cut down on the need to climb all those damn stairs.
Both Nick Dumas and Christopher Moore have pointed out to me that Graham Baxter's arrangement is actually the way the designers intended. The problem is that the diagram is confusing. Please find below a modified diagram that makes things clear.
And of course we cannot forget the internal centrifuge in the good spacecraft Discovery.
After lunch, from 1300 to 1600 Bowman would make a slow and careful tour of the ship - or such part of it as was accessible. Discovery measured almost four hundred feet from end to end, but the little universe occupied by her crew lay entirely inside the forty-foot sphere of the pressure hull.
Here were all the life-support systems, and the Control Deck which was the operational heart of the ship. Below this was a small "space-garage" fitted with three airlocks, through which powered capsules, just large enough to hold a man, could sail out into the void if the need arose for extravehicular activity.
The equatorial region of the pressure sphere - the slice, as it were, from Capricorn to Cancer - enclosed a slowly rotating drum, thirty-five feet in diameter. As it made one revolution every ten seconds, this carrousel or centrifuge produced an artificial gravity equal to that of the Moon. This was enough to prevent the physical atrophy which would result from the complete absence of weight, and it also allowed the routine functions of living to be carried out under normal - or nearly normal - conditions.
The carrousel therefore contained the kitchen, dining, washing, and toilet facilities. Only here was it safe to prepare and handle hot drinks - quite dangerous in weightless conditions, where one can be badly scalded by floating globules of boiling water. The problem of shaving was also solved; there would be no weightless bristles drifting around to endanger electrical equipment and produce a health hazard.
Around the rim of the carrousel were five tiny cubicles, fitted out by each astronaut according to taste and containing his personal belongings. Only Bowman's and Poole's were now in use, while the future occupants of the other three cabins reposed in their electronic sarcophagi next door.
The spin of the carrousel could be stopped if necessary; when this happened, its angular momentum had to be stored in a flywheel, and switched back again when rotation was restarted. But normally it was left running at constant speed, for it was easy enough to enter the big, slowly turning drum by going hand-over-hand along a pole through the zero-gee region at its center. Transferring to the moving section was as easy and automatic, after a little experience, as stepping onto a moving escalator.
I have thought up a not terribly original variant on the gimbaled centrifuge that I call "Ezekiel's Wheel". Imagine a classic centrifuge ship, resembling a pencil stuck through a doughnut. Imagine that the doughnut is actually sliced through to form six or so radial segments (i.e., cut the doughnut like it was a pie). For gimbaling, rotate each segment along their long axis so that the rim faces towards the engine. This is the configuration for thrust gravity.
The hard part is the mechanism that allows the segments to pivot. However, that has been solved by Josef F. Blumrich, formerly of NASA. His patent 3,789,947 is for a "unidirectional wheel", but for our purposes it includes a design for the pivot mechanism.
Using the Blumrich rim segment mechanism for gimballing the centrifuge results in the following monstrosity:
Each of the green habitat modules can rotate around their long axis to accommodate the current direction of "down".
The main problem is sometimes the floor is not level.
In the diagram, note that the floor (which the little man is standing on) is curved. As in all centrifuges, this ensures that the floor will seem flat while under spin (that is, if you place a ball on the floor it will stay put). Unfortunately, when the spin stops and the habitat modules rotate down for thrust gravity, the floor will seem like valleys. If you place a ball on the edge of the habitat floor, the ball will roll "downhill" to the center floor of the module.
Or you could have it the other way. Make the floor straight instead of curved. This way it will seen flat while under thrust. However, under spin, the floor will seem curved like a hill. If you place a ball on the center of the habitat floor, it will roll "downhill" to one of the two edges. This is because the strength of spin gravity depends upon the distance to the spin axis, and the two edges are farther away from the axis than the habitat floor center.
The only solutions I've manage to think up involve dynamically altering the contour of the floor, or making each habitat segment narrow enough that the slope is manageable (which is the solution used by the Pilgrim Observer and Dream Pod 9).
Making Do Without
As always, Ken Burnside has some insightful and pragmatic concerns about the topic at hand:
I have a very basic problem with spin sections in spaceships.
1) The more things are meant to move, the more they wear out. Making a gimbaled joint that doesn't become the maintenance nightmare of the F-14 swing-wing is a tricky proposition -- particularly in space where there's vacuum welding, thermal differences from ambient solar radiation, and worse.
2) How the heck do you get the plumbing to work? I guarantee you that rotating your typical bathroom through 90 degrees will make every water conveyance run wrong. Not to mention the times in transition when it'll be at zero gee.
Or do you put in twice as many bathrooms?
The reason why ships in Ten Worlds don't have spin sections come from the maintenance issues, the fact that the trips themselves are months, not years in duration and that most of the waypoints have spin gravity on can cities.
And the "90 degree off-axis aggressive maneuvers with the portapotty" problem.
On a related note, when your spin section arms are extended out, where do your radiators go?
Guido Lißmann notes that the plumbing problem has a couple of solutions. Route the pipes through the pivot center with some kind of rotating sleeve, have self contained plumbing systems totally within the centrifuge, or resort to chemical toilets like used in passenger aircraft.
It is tempting to just forget about spin gravity, and just have everybody float around while the ship is not under thrust. While it is true that after about a year in free-fall the human body starts to suffer bone decalcification and other damage, one can assume that future medical will have discovered a treatment. Marshall Savage suggests electro stimulation therapy of the muscles (Ken Burnside says rocket crewmen will have to wear their "jerk-jammies" when they sleep). One would hope that a medical cure will be found for the nausea induced by free fall, or "drop sickness" (they say that the first six months are the worse).
And prior to (the) Mercury (program) we hadn't any real experience at all. We flew transport planes in parabolic courses that might give as much as 30 seconds of almost-zero-g, and that was all we knew. I will not soon forget some of our early low-g experiments. Some genius wanted to know how a cat oriented: visual cues, or a gravity sensor? The obvious way to find out was to take a cat up in an airplane, fly the plane in a parabolic orbit, and observe the cat during the short period of zero-g.
It made sense. Maybe. It didn't make enough that anyone would authorize a large airplane for the experiment, so a camera was mounted in a small fighter (perhaps a T-bird; I forget), and the cat was carried along in the pilot's lap. A movie was made of the whole run.
The film, I fear, doesn't tell us how a cat orients. It shows the pilot frantically trying to tear the cat off his arm, and the cat just as violently resisting. Eventually the cat was broken free and let go in mid-air, where it seemed magically (teleportation? or not really zero gravity in the plane? no one knows) to move, rapidly, straight back to the pilot, claws outstretched. This time there was no tearing it loose at all. The only thing I learned from the film is that cats (or this one anyway) don't like zero gravity, and think human beings are the obvious point of stability to cling to...
What is so funny about a man being dropsick? Those dolts with cast-iron stomachs always laugh - I'll bet they would laugh if Grandma broke both legs.
I was spacesick, of course, as soon as the rocket ship quit blasting and went into free fall. I came out of it fairly quickly as my stomach was practically empty - I'd eaten nothing since breakfast- and was simply wanly miserable the remaining eternity of that awful trip. It took us an hour and forty-three minutes to make rendezvous, which is roughly equal to a thousand years in purgatory to a ground hog like myself.
I'll say this for Dak, though: he did not laugh. Dak was a professional and he treated my normal reaction with the impersonal good manners of a infight nurse - not like those flat-headed, loud-voiced jackasses you'll find on the passenger list of a Moon shuttle. If I had my way, those healthy self-panickers would be spaced in mid-orbit and allowed to laugh themselves to death in vacuum.
Despite the turmoil in my mind and the thousand questions I wanted to ask we had almost made rendezvous with a torchship, which was in parking orbit around Earth, before I could stir up interest in anything. I suspect that if one were to inform a victim of spacesickness that he was to be shot at sunrise his own answer would be, "Yes? Would you hand me that sack, please?"
"Dak?" I said as he signed off.
"Later," he answered. "I'm about to match orbits. The contact may be a little rough, as I am not going to waste time worrying about chuck holes. So pipe down and hang on."
And it was rough. By the time we were in the torchship I was glad to be comfortably back in free fall again; surge nausea is even worse than everyday dropsickness.
A possible compromise is the personal centrifuge. This is a centrifuge a few meters long, just big enough for one man to strap in, spin up about 30 RPM, and do some exercises. Yes, this will probably give them severe motion sickness, but it will only be for the duration of the exercise period.
Free-Fall vs. Zero-G
As a side note, the proper term is "free-fall", since "zero-g" is not quite correct. The crewmembers of the International Space Station are in a gravity field almost as strong as the one you are in. They float around and you don't since they are "falling" and you are not.