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.
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:
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":
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.
And of course we cannot forget the internal centrifuge in the good spacecraft Discovery.
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.
|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).
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.
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.
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).
The main design problem when adding artificial gravity to a spacecraft is that the direction of "down" while under thrust is not the same as the direction of "down" while under spin gravity. And the direction of "down" while under both thrust and spin gravity was at an angle between the two (the vector sum of the two accelerations). This can get confusing.
Why is this a problem? What was a floor under thrust might turn into a wall under spin gravity. So which surface do you mount the toilet on? If the designer is not careful, half the time the toilet will be sideways and pouring water all over the floor.
A similar problem happens with belly landers: the direction of "down" while under thrust is at ninety degrees to the direction of "down" when sitting on the runway impersonating an aircraft.
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. Not to mention the toilets.
The alternative is rotating the entire room on gimbals, or using a gimballed centrifuge.
NASA's old Space Shuttle had the belly lander problem. They dealt with the problem by mostly ignoring it. The Shuttle's habitat module was laid out for "belly is down" mode. It was only subjected to "thrust is down" mode while sitting on the launch pad and during the boost into orbit. That period of time was only a fraction of the total mission time, and the astronauts were to spend that time strapped into their acceleration couches anyway. They made do with a few ladders to climb into their couches.
The pilots just had to learn how to deal with flying the shuttle on their backs with the control panels above them during lift off, and flying the shuttle on the seat of their pants with the control panels in front of them during the dead-stick landing.
This design is from a book called First Men to the Moon (1958) written by a certain Wernher von Braun, aka "The Father of Rocket Science" and the first director of NASA. The book came out shortly after the Sputnik Crisis.
Their solution to the "which way is down?" problem is to put the crew's seats on tracks. The track was shaped like a letter "L", with one track at 90° to the ship's tail (thrust axis) and the other at 90° to the ship's belly. While landing on its belly the seat would be on the belly track. While being a tail lander on the lunar surface, the seat would be on the tail track. During lift off for some odd reason the seat would be on the tail track but tilted back at 45°.
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.
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.
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 .
As always, Ken Burnside has some insightful and pragmatic concerns about the topic at hand:
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).
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.