Introduction

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. 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.

Spin Grav Math

For 1.0 g of Artificial Gravity
Rotation
Rate
(rpm)
Radius
(m)
1895.47
2223.87
399.50
455.97
535.82
624.87
718.27
813.99
911.06
108.95

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))

where

  • 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."

From SPACE CADET by Robert Heinlein (1948)

Problems with Spin Grav

Coriolis Effect

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.

Spin RPM Limit

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 RateGravity
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.

Troy Campbell

Which Way Is Down?

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.

First Men to the Moon

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°.

Space Angel

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.

R/P FLIP

The Scripps Institution of Oceanography's FLIP ship does things the brute force way. Notice the two sinks at ninety degrees to each other. It features doors in the floor, portholes in the ceiling, tables bolted sideways to walls, and stairs leading to nowhere.

BIS Lunar Spaceship

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.

Polygon Centrifuge

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 .

Spin Grav Types

Dependent Centrifuge

Trying to make artificial gravity by spinning the ship add entire new categories of headaches for ship designers.

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":

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.

Guido Lißmann

The landing boat overtook Discovery from below and behind, giving Drake a good look at his ship. The battle cruiser consisted of a torpedo-like central cylinder surrounded by a ring structure. The central cylinder housed the ship’s mass converter, photon drive, and jump engines — the latter needing only an up-to-date jump program to once more hurl the ship into the interstellar spacelanes. In addition, within the cylinder were fuel tanks filled with deuterium and tritium enriched cryogen; the heavy antimatter projectors that were Discovery’s main armament; and the ancillary equipment that provided power to the ship’s outer ring.

The surrounding ring was supported off the cylinder by twelve hollow spokes — six forward and six aft. It contained crew quarters, communications, sensors, secondary weapons pods, cargo spaces, and the hangar bay in which auxiliary craft were housed.


Drake listened to the communications between the landing boat and the cruiser all through the approach. As they drew close, he noticed the actinic light of the ship’s attitude jets firing around the periphery of the habitat ring. When in parking orbit, the cruiser was spun about its axis to provide half a standard gravity on the outermost crew deck. The purpose of the attitude jets was to halt the rotation in preparation for taking the landing boat aboard.


There is a common belief among the uninitiated that a spaceship’s control room is located somewhere near the ship’s bow. In truth, that is almost never the case. Discovery, with its cylinder-and-ring design, was particularly unsuited to such an arrangement. Like most warships, the cruiser’s control room was located in the safest place the designers could find to put it — at the midpoint of the inside curve of the habitat ring.

Actually, Discovery possessed three control rooms, each capable of flying or fighting the ship alone should the need arise. For normal operations, however, there was a traditional division of labor between the three nerve centers. Control Room No. 1 performed the usual functions of a spacecraft’s bridge (flight control, communications, and astrogation); No. 2 was devoted to control of weapons and sensors; and No. 3 was used by the engineering department to monitor the overall health of the ship and its power-and-drive system.


An hour later, the ship was accelerating along a normal departure orbit at one standard gravity while crewmen rushed to convert compartments from the “out is down” orientation of parking orbit, to the “aft is down” of powered boost. The only compartments that did not need conversion were the control rooms (which were gimbaled to automatically keep the deck horizontal) and the larger compartments (hangar bay, engine room), which had been designed to allow access regardless of the direction of “down.”


Their destination was Alexandria’s main ballroom. Situated on the outermost level (where gravity was highest), the ballroom was large enough for the deck underfoot to show a perceptible curve. In order to use the large compartment, however, it was necessary that ship’s spin provide the pseudo-gravity. During powered flight, when gravity was ‘aft’ rather than ‘out’, the compartment was a deep arc-shaped well of limited utility. Since no spaceship can afford to waste that much space, the architects who designed the liner had installed four levels of retractable decks. Once extended from their recesses in the walls, they turned the oversize compartment into a series of smaller spaces.

From Antares Dawn by Michael McCollum (1998)

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.

Martin Marietta Study

A variety of Artificial gravity (AG) / Mars transfer vehicle (MTV) concepts were developed by the Martin Marietta Astronautics Group for NASA’s Mars Exploration Case Studies in 1988 – 89. Each of these concepts used a large diameter (~39 – 46 m) aerobrake (AB) with a low lift to drag (L/D) ratio of ~0.2 for Mars orbit capture (MOC). These large ABs required assembly in LEO before being outfitted with habitation, auxiliary PVA power and chemical propulsion system elements within their protective envelope. By rotating the AB about its central axis at different spin rates and mounting the habitat modules near the outer perimeter of the AB to increase the rotation radius, a range of centrifugal forces can be generated for the crew during the transit out to Mars and back. A sampling of these AB concepts (minus their multiple expendable trans-Mars injection (TMI) stages) is shown in Fig 1.

Concept 1 was developed for a large crew of 12 – 18 astronauts. It carried eight cylindrical Space Station Freedom (SSF)-type habitation modules arranged in a ring to provide a 100-m long circular jogging track. The modules were mounted to a large 45.6-m diameter AB sized for aerocapture at both Mars and again at Earth for spacecraft recovery and possible reuse. This very large spacecraft had an initial mass in low Earth orbit (IMLEO) > 1500 metric tons (1 t = 1000 kg).

Concept 2 carried 8 astronauts and used four SSF habitat modules arranged in a “Bent-I” configuration inside a 41-m diameter AB. Two pressurized tunnels connected the four habitat modules to a central logistics and docking hub to which the Mars Descent / Ascent Vehicle (MDAV) was attached. The IMLEO for Concept 2 was ~1091 t.

Concept 3 utilized a deployable flexible fabric AB (~39-m in diameter) and carried two cylindrical hab modules each with five separate floors arranged perpendicular to the modules’ long axis. The modules were attached to the central logistics and docking hub using swivel joints allowing them to swing outward to increase their rotation radius during AG operation. The modules were cranked back inside the protective envelope of the AB prior to MOC. The modules housed 5 - 7 crew and the total mission IMLEO was ~687 t including the four expendable TMI stages.

Concepts 4 and 5 used dual retractable tethers to separate paired or individual hab modules from the AB and primary propulsion system. With tether lengths of approximately several hundred meters, rotations rates as low as 2 revolutions per minute (rpm) could provide ~1-g of centrifugal acceleration for the crew.

Each of the above concepts had a number of drawbacks. Concepts 1 and 2 were very large, required significant orbital assembly for the AB and overall vehicle, and had large IMLEO requirements (>1000 t). Concept 3 required an internal arrangement for the hab modules that differed from that of the SSF habitation modules used in the other designs. It also required movement of two major pressurized mechanical joints. With tethered Concepts 4 and 5, the reaction control system (RCS) propellant requirements to initiate and stop vehicle rotation were larger, and the dynamic control problems more severe during the deployment and retraction process, as well as during vehicle spin up and spin down. A tether break or reel freeze-up could also be a critical failure mode. From an operational standpoint, once deployed, the crew in Concept 4 would be isolated from the systems enclosed within the aerobrake (e.g., MDAV) and in Concept 5, isolated from each other as well.


To avoid the deficiencies of the above concepts, Martin Marietta proposed Concept 6, an AG/MTV design that used chemical propulsion and carried twin cylindrical SSF habitation modules whose long axes were oriented perpendicular to the longitudinal spin axis of the MTV – referred to as the Dumbbell B configuration (Fig. 2). The hab modules were connected to a central logistics and docking hub by two pressurized tunnels each ~12.5 m long. Each hab module – designed to accommodate 2 - 3 crewmembers – had excess capacity so that either could serve as a safe haven for the entire crew in case of an emergency. Attached to the Sun-facing side of each tunnel and hab module were ~30 m2 and 75 m2, respectively, of PVAs producing ~26 kWe of electrical power for the spacecraft’s various systems. Once fully assembled, the rotation radius from the center of the logistics module to the floor of each hab module was ~17 m allowing centrifugal acceleration levels ranging from 0.38-g to 0.68-g for vehicle spin rates of 4.5 to 6 rpm. At a slightly higher spin rate of 7.25 rpm, 1-g could be achieved. The pressurized logistics hub also provided a shirt-sleeve environment and anytime crew access to the MDAV docked to the front of the vehicle.


General Design Principles

  • Hab Modules should have their major dimension / traffic pattern parallel to the vehicle's spin axis
  • Radial traffic flow should be minimized
  • Orient command / work station displays vertically to minimize left-right head rotations — lateral axis through ears should be parallel to spin axis
  • Orient sleeping bunks parallel to spin axis
  • Minimize visual stimuli (windowless crew cabins)

Radial Orientation

  • Multi-level vertical design
  • Large gravity gradient
  • Ladders between levels
  • Tangential and Transverse Coriolis effects
  • Potentially simpler payload (PL) & SC design Earth Orbit Rendezvous and Dock (EOR&D)

Axial Orientation

  • Uni- or bi-level horizontal layout design
  • Minimal gravity gradient
  • Long transfer tunnel to central connecting hub
  • Minimal Coriolis effects
  • More complex PL & SC design (on-orbit assembly)

Tangential Orientation

  • Uni- or bi-level horizontal layout design
  • Minimal gravity gradient
  • Long transfer tunnel to central connecting hub
  • Coriolis effects
  • More complex PL & SC design (on-orbit assembly)

In designing an AG spacecraft, a number of important human factors must be taken into account in selecting the rotation radius, angular velocity, and g-levels. These factors include the gravity gradient effect, Coriolis forces and cross-coupled acceleration effects. These human factor effects also come into play when considering the orientation of the habitat module or modules (shown in Fig. 5) relative to the spin axis of the vehicle. Orientation options include:

  1. Radial (used by Concept 3, the von Braun and Copernicus-B)
  2. Tangential (used in Concepts 1, 2, 6 and the A. C. Clark) – also referred to as the Dumbbell B configuration
  3. Axial (used in Concepts 4, 5, and a variant of the A. C. Clark) – referred to as the Dumbbell A configuration

The radial habitat module is by definition a multi-level vertical design. Because the centrifugal acceleration varies directly with the radial distance from the center of rotation, a vertical gravity gradient will exist between the different levels of the hab module(s) and even along the human body itself. Crewmembers climbing “up” a radial-oriented ladder toward the vehicle’s center of rotation would lose weight with each step. Awkward materials handling problems and uneven g-loadings on the body are also possible but are not expected to be significant on AG vehicles with reasonable rotation radii.

Tangential Coriolis forces will also expose the crew to pseudo weight changes depending on their direction of motion with respect to the spin axis of the vehicle. While no Coriolis force occurs when walking parallel to the spin axis, astronauts will feel heavier when moving in the direction of vehicle rotation and lighter when walking in the reverse direction. Transverse Coriolis forces will be experienced by astronauts moving vertically between habitat levels. When climbing “up” toward the vehicle’s center of rotation, the astronauts will be pushed sideways in the direction of spacecraft spin. A sideways push away from the spin direction will be felt when climbing “down” the ladder (refer to Fig. 6).

Lastly, cross-coupled angular acceleration effects will be experienced by astronauts early on due to head movement in the directions transverse to the axis of rotation and the primary direction of spacecraft flight. With time and use of distinctive interior color schemes or wall-mounted designations to help identify spin direction (depicted in Fig. 6), astronauts should be able to compensate for and acclimate to these AG effects. General design principles for habitats onboard rotating AG spacecraft were provided by Loret and are summarized in Fig. 5.

Despite the lack of current experimental data needed to establish accepted g-threshold requirements and other operational characteristics (e.g., rotation radius and ω), previous experts in this area used existing physiological and/or human factors data coupled with reasonable assumptions to identify representative operational regions for AG vehicles. Stone and Thompson recommended a rotation radius ≥ 14.6 m and a spin rate ≤ 6 rpm, while Shipov thought that the minimum radius should be ~20 m.

During the 1960’s, researchers at the Naval Medical Research Laboratory in Pensacola, Florida used their Slow Rotating Room (SRR) to study the acute rotation effects phenomena at rates as high as 10 rpm. Their results indicated that a judicious restriction of head motions and progressive adaptation through stepwise increases in spin rate (1 rpm every 2 days during 16 days of rotation) allowed most human subjects to adjust quickly to avoid the adverse physical symptoms of higher rotation rates. “Later studies have expanded on the experience from that time and demonstrated that complete adaptation to rotation rates as high as 10 rpm can be achieved within minutes if repeated voluntary movements are made. Such movements were avoided in the early Pensacola studies.”

Bola

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."

Tumbling Pigeon

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.

Independent Centrifuge

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.

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.

From 2001 A Space Odyssey by Sir Arthur C. Clarke (1969)

Gimbaled Centrifuge

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.

Pilgrim Observer

Pilgrim Observer
LevelDist from
center
Centrifugal
Accel
Gravity
Level 610.16 m0.447 m/s0.05g
Level 512.70 m0.559 m/s0.06g
Level 415.24 m0.671 m/s0.07g
Level 317.78 m0.782 m/s0.08g
Level 220.32 m0.894 m/s0.09g
Level 122.86 m1.006 m/s0.10g

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.

Graham Baxter

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.

Ezekiel's Wheel

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?

Ken Burnside

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).

Free-Fall Cat 1

(ed note: this is science fact, not science fiction)

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...

(ed note: the Lockheed F-94C Starfire was developed from the Lockheed T-33 "T-bird", and they look remarkably alike. So I am pretty sure the photo is from the movie Dr. Pournelle mentions.

On the other hand, here they say general free-fall experiments were started using a Lockheed T-33 "T-bird", went to using an F-89, then ended up using a Lockheed F-94C Starfire. So Dr. Pournelle might have actually seen a T-bird after all, and the photo is from a totally different test. )

From A Step Farther Out by Jerry Pournelle, 1979.
Free-Fall Cat 2

Actual unethical experiment story here, complete with results:

My dad was a skydiver back in the sixties. There was a guy in his club that was a nut. He had the idea that he could test the axiom that "cats always land on their feet" from free fall altitude, where he would fall with them and observe their self-righting behavior. He had no interest in aiding their descent, just wanted to see how they behaved in free fall. In his plan, landing was the cats' problem, not his. Scientific impartiality, or some such thing.

He took four stray cats up in a pillowcase for the jump. After exiting the plane, he turned the pillowcase inside out, releasing the cats. To his great surprise, all four cats attached themselves to his body immediately. With their claws. Given that cats have 18 claws each, he was punctured at least 72 times. More, probably, because he struggled vainly to remove the cats as he fell, but they were having none of it, and would reattach with even more conviction with every effort he made to pull them off.

Presently, he was out of altitude, and had to turn his attention to opening the chute. Let's pause to do some math. A chute opening can generate as much as 3 Gs of force. The average cat weighs 8 lbs at 1 G. At three Gs, this becomes 24 lbs per cat. So when the chute opened, for a moment this guy had 72 razor sharp claws in his skin, each one being pulled down with a force of about one and a third pounds. That's 96 pounds of cat. He was sliced to ribbons, basically.

All four cats hung on through the chute opening, although the skydiver's shredded flesh allowed each one to slip several inches. Bleeding and in misery, the skydiver managed to make a safe, if rather rough, landing in a farm field.

As soon as he hit the earth, all four cats ran off across the field, leaving him to lie there bleeding from his hundred or so wounds.

He was the only member of the skydiving club that was displeased with the results of his experiment.

(ed note: RocketCat is of the opinion that the experimenter got off way too lightly. RocketCat then left to hunt down the experimenter and teach him the error of his ways...)

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.

From DOUBLE STAR by Robert Heinlein, 1956

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.

Magnetic Boots

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.

In some old SF novel I read decades ago the suits had magnets in the toes but not the heels, in order to make it easier to pull the boot magnet off the floor so you can walk. Or maybe it was the heel but not the toe. Anyway I cannot remember which novel it was, drop me a line if you know.

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.

2001 A Space Odyssey

The stewardess came walking up the narrow corridor to the right of the closely spaced seats. There was a slight buoyancy about her steps, and her feet came away from the floor reluctantly as if entangled in glue. She was keeping to the bright yellow band of Velcro carpeting that ran the full length of the floor - and of the ceiling. The carpet, and the soles of her sandals, were covered with myriads of tiny hooks, so that they clung together like burrs. This trick of walking in free fall was immensely reassuring to disoriented passengers.

From 2001 A Space Odyssey by Arthur C. Clarke (1969)
Leviathan Wakes

As they walked thorugh a maze of corridors, the ship started a slight vibration, and gravity slowly reappeared. They were under thrust. Holden used his heels to touch his boots' slide controls, turning the magnets off.

From Leviathan Wakes by James Corey (2011)
Space Cadet

“Click on,” directed the instructor, and placed his boots gently against the side of the lock. Matt did likewise and felt the magnetic soles of his boots click against the steel. “Follow me and stay closed up.” Their teacher walked along the wall to the open door and performed an awkward little squatting spread-eagle step. One boot was still inside the door, flat to the wall, with the toe pointing inboard; with the other he reached around the corner, bent his knees, and felt for the outer surface of the ship. He withdrew the foot still in the lock and straightened his body-with which he almost disappeared, for he now stuck straight out from the ship, his feet flat to her side.

Following in order, Matt went out through the door. The ninety degree turn to get outside the lock and “standing” on the outer skin of the ship he found to be tricky; he was forced to use his hands to steady himself on the door frame. But he got outside and “standing up.” There was no true up-and-down; they were still weightless, but the steel side was a floor “under” them; they stuck to it as a fly sticks to a ceiling.

Matt took a couple of trial steps. It was like walking in mud; his feet would cling stickily to the ship, then pull away suddenly. It took getting used to.

From SPACE CADET by Robert Heinlein (1948)
Space Angel

Last of all, Torwald took Kelly to the rear of the shop, where the footwear was kept. They rummaged around for a few minutes while Torwald gave him a running lecture on the virtues of good boots.

"You might not think so, kid, but boots are more important than any other item of a spacer's equipment. That's because you never know when you may be set afoot, or in what terrain, or in what climate." Kelly didn't like the sound of the expression "set afoot."

"Besides," Torwald continued, "a spacer has very little to do with space, any more than a sailor has with water. It's just something to get across to reach the planets, where the jobs are. And on the ground, you need boots. Aha, jackpot!" With that exclamation, he pulled a pair of boots from a bin. "Genuine pre-War unissued Space Marine boots!"

"How can you tell they're pre-War?" Kelly asked, sorting through the bin to find a pair that fit. Torwald turned a boot sole-up.

"See those little threaded holes? That's where they used to screw in the magnetic plates. They haven't used those plates in fifty years, but the Navy required that the mounts be left there in case of equipment failures. When the War came along, they dropped that reg, and a lot of quality, to cut costs. These boots will last you a lifetime."

From Space Angel by John Maddox Roberts (1979)

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