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. Nothing short of a freaking torchship can do 1 g of acceleration for longer than a few minutes, and it is highly inconvenient to cart along a planet the size of Terra just so you can have some gravity.
Science fiction authors find all these choices to be confining, so they have invented all sorts of technobabble ways of generating gravity with the flip of a switch.
The small reason to put artificial gravity on your spacecraft is because it makes things like preparing food and urinating easier. But the big reason is that microgravity does hideous long term damage to the human organism.
With centrifugal gravity, the direction of "down" is in the opposite direction of the spin axis of the centrifuge (in a direction at 90° to the spin axis, pointing away from it). Unless you are doing something silly like using rocket acceleration at the same time with a centrifuge that is not gimbaled.
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.
The Coriolis Effect is due to "rotating frames of reference", the latter means that if you are spinning around but think you are stationary, the universe looks weird. The Coriolis effect is one of the three "fictious forces" that rotating frames of reference is prone to (one of the other fictious forces is the centrifugal forces being used for artificial gravity).
But you really do not need to know all of this. The point is that inside a centrifuge or other spinning method of creating artificial gravity, moving objects appear to move in curves instead of straight lines. I mean other than the ordinary curve you see when you throw a ball and gravity tugs it down to the ground.
The practical point is the list of moving objects whose path curves due to the coriolis effect includes the fluids in one's inner ear. Which can cause nausea.
Refer to Figure 1. It is a large spinning disk like a merry-go-round. There is a person standing on the red dot. There is a black ball at the center which moves to the rim.
To an outside observer, they see the disk and the person spinning, and the black ball moves in a straight line.
But to the person on the red dot, they see themselves and the disk as stationary, and the black ball moves in a curve.
You can see this yourself if you go to a children's playground that still has an old fashioned merry-go-round, sit on it, spin it up, then start throwing some balls. Weird, huh?
The amusing effects are the crazy trajectories of thrown objects, such as the whisky being poured in the image above. However it is not so amusing if the moving object is a bullet. If you fire a slugthrower inside a spinning habitat you will miss every time until you learn to correct for the Coriolis effect.
Refer to Figure 2. In a spinning space habitat, tossing a ball towards the spin axis makes it travel to the opposite side. But from the person spinning inside, the ball appears to loop-the-loop. The ball is traveling at such a speed that the time it takes to go from one side to the other is the same time as one-half the habitat's spin rate. If a bullet was traveling at the same rate you could inadvertently shoot yourself (in practice the habitat would have to be spinning rather rapidly and bullet traveling rather slow).
Other moving objects with their trajectories curved by the Coriolis effect include your arms and legs.
As it turns out, there are limits on the rotation rate. The Coriolis effect can induce nausea. Sort of like spin motion-sickness. You do not want a bunch of green-faced astronauts/star-liner passengers/space habitat colonists moaning that they are going to die and vomiting everywhere.
The only way to increase gravity (Ca) without increasing the RPMs (Cr) is to increase the spin radius (Cl). What this means is you take the required gravity and the maximum rotation rate allowed, plug it into the Cl = Ca / (0.011 * Cr2) equation, and you'll see what sort of spin radius you will have to deal with.
If the spin radius is too huge (I don't wanna blasted spaceship with a centrifuge two-hundred freaking meters radius!), you'll have to decrease the amount of gravity, increase the rotation rate, or both. That or put up with a lot of vomiting astronauts.
According to Space Settlement Population Rotation Tolerance the safe spin limits are:
- Up to 2 rpm should be no problem for residents and require little adaptation by visitors.
- Up to 4 rpm should be no problem for residents but will require some training and/or a few hours to perhaps a day of adaptation by visitors.
- Up to 6 rpm is unlikely to be a problem for residents but may require extensive visitor training and/or adaptation (multiple days). Some particularly susceptible individuals may have a great deal of difficulty.
- Up to 10 rpm adaptation has been achieved with specific training. However, the radius of a space colony at these rotation rates is so small (under ~20 m for seven rpm) it’s hard to imagine anyone wanting to live there permanently, much less raise children. But military personnel could be trained to tolerate it.
Discovery Radius 5.5 m Rotation Rate Gravity 7.5 (rpm) 0.347 gs 8 (rpm) 0.395 gs 9 (rpm) 0.500 gs 10 (rpm) 0.617 gs
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.
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 gimbaled 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. Details can be found in Self-deploying space station final report .
But there is 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 in all parts of the wheel, the station has to be a circle. That is the only shape where the all parts of the rim are the same distance from the axis.
The point is, with a hexagon, different parts of the rim are at different distaces from the axis, and so have different gravities.
Now, look at the first image below. 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 (i.e., the longer the green line, the more intense the gravity). 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.
I was curious as to how much of a problem this actually was. After doing some trigonometry (with no help from my parents) my questionable results are that for a hexagonal station, the gravity will vary between 100% and 113%. This is only about ten percent, which is annoying but probably not a show-stopper.
At point A gravity is at 100%, whatever the station is spun up for.
Point B is 15 degrees counter-clockwise from A, so in right triangle ABX if adjacent side (line AX) is of length 1.00, then the hypotenuse (line BX or distance from the spin axis) is 2.00 - cosine 15° or 1.03. Therefore gravity is 103% (because according to the equation the gravitational acceleration is proportional to the distance from the spin axis).
Point C is 30 degrees counter-clockwise. This hypotenuse is 1.13 so the gravity is 113%
Again this is only a difference of 13%, but things dropped on the floor are going to accumulate at the station hexagon vertices as they roll downhill.
If a spacecraft (with spin gravity or not) was slammed by a foreign object hard enough to start the spacecraft tumbling, this will generate unexpected spin gravity. This is pretty much guaranteed to create an emergency situation inside the ship.
This is highly unlikely to occur naturally.
But when Zane Mankowski started working with his simulation game, he discovered that this was rather common when low mass combat spacecraft were struck.
The most common arrangement are ships that spin on their long axis, that is, the thrust axis. This is a "dependent centrifuge", that is, the centrifuge is the entire ship. Independent centrifuges are where the spacecraft proper does not spin, but the centrifuge spins indepenently of the spacecraft.
Spin gravity is usually at ninety degrees to thrust gravity.
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.
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.
An independent centrifuge is where only part of the ship is spun for gravity while the rest stays stationary. As opposed to dependent centrifuges where the entire ships spins.
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.
Gimbaled Centrifuges are attempts to deal with the "which way is down?" problem. As a general rule they are hideous engineering challenges and maintenance nightmares.
|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". Be told that when I show this design to real engineers they laugh themselves silly, mostly due to the reasons given by Ken Burnside.
Remember the basic problem is that the direction of "down" is different under thrust than it is under spin gravity.
A gimbaled centrifuge uses long slabs for the centrifuge, rotating them to change from thrust mode to spin mode. The trouble is that slabs are a very inefficient use of habitat space. It would be nice if you could somehow rotate the orientation of a doughnut shaped centrifuge.
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). See the green parts in the diagram to the right. For gimbaling, rotate each segment along their long axis to switch modes. Note red arrow for "direction of 'down' while thrusting" and yellow arrow for "direction of 'down' while spinning".
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.
The gold wheels in Blumrich's mechanism allow the green centrifuge segments to rotate for mode changing. Yes, this is a monstrous Rube Goldberg contraption but you can't have everything.
The main problem is sometimes the floor is not level. In other words, the blasted thing is a polygon centrifuge.
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).
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.
In lieu of a habitat module on a centrifuge, under acceleration, or equipped with technobabble paragravity; science fiction novels often equips the crew with magnetic boots/sandals and a ferromagnetic floor.
Magnetic boots sometimes appear on space suits as well, assuming the hull is constructed out of something ferromagnetic. But magnets do not work very well on hulls composed of titanium, aluminum, magnesium or other space age materials.
If one does have a ferromagnetic hull, it might be best to have magnets just in the boot heels but not the toes, to facilitate walking. The idea is that if a boot is attached to the hull, you can release it by pushing down with your toes and lifing your heel, using a natural walking motion to detach the magnetic heel. Then the boot moves forward, approaching the hull heel-first. This allows the magnet in the heel to attach. At least that's how I remember it, maybe it is the other way around.
In The Expanse, the magnetic boots were electromagnets, so you could turn them on or off. They had red indicator lights and a switch one could operate by tapping boots.
In the movie 2001 A Space Odyssey the stewardess wore velcro footies to walk on the velcro floor.
But it is good to keep in mind that they do not use any of these on the International Space Station. They just float everwhere and to heck with walking. Besides, magnetic fields interfere with navigation and communication systems.