## 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)
(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.

## 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.

### Gyroscopic Precession

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. The obvious solution is to have two counter-rotating centrifuges, so their torque cancels out. Just like Contra-rotating propellers on an airplane. Alternatively you can use one centrifuge plus a monstrous counter-rotating flywheel with the same mass.

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. The technical term is gyroscopic precession. Rev up a toy gyroscope and try to turn it and you'll see what I mean.

The solution to that 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.

Bottom line:

Centrifuge Correction
Relative MassSolution
Centrifuge is large percentage of ship massReaction Control System thrust is skewed 90°
Centrifuge is tiny percentage of ship massHave two counter-rotating centrifuges

### Spin Balance

Another problem is Spin 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. The centrifuge could wobble: making the gravity uneven, causing structural damage/centrifuge destruction, and causing the center of gravity to oscillate.

The latter means the center of spin will wander around instead of being rigidly located at the designed spin axis. Which can be a real problem if the spin axis has the docking port. The situation will be just as nasty if the centrifuge is a wheel space station with a spacecraft landing bay at the spin axis. Generally the landing bay is de-spun by spinning contrary to the centrifuge, so incoming spacecraft can land in something stationary. If the space station is wobbling, so will the landing bay. Docking will be much more dangerous than a fighter jet trying to land on the deck of a sea-going aircraft carrier during a typhoon.

Even worse, spacecraft tend to have optimized structural support because every gram counts. The ship's spine will be very strong along the thrust axis, but being jerked sideways by an oscillating centrifuge could snap the spine like a piece of uncooked spaghetti.

Load balancing could be accomplished by a series of ballast tanks and a network of pipes to pump water from one tank to another. In NASA-speak, these are called ballast trim tanks.

### Braked Centrifuge

When an independent centrifuge is braked to a halt (or if a derelict spacecraft has a spinning centrifuge that gradually brakes due to friction in the bearings), the conservation of angular momentum makes the entire ship spin on the centrifuge's rotational axis.

Since most independent centrifuges are attached to the ship much like a wheel spinning on a fixed axle, the ship will start spinning on its long axis. A crewed ship will use their reaction control system to stop the spin. A derelict that is abandoned (or crewed with the dead) will of course just keep spinning on its long axis.

Which is why people who watched the movie 2010: The Year We Make Contact were puzzled by the sight of the Discovery flipping end-over-end like a blasted baton twirler's baton.

Discovery's independent centrifuge is mounted in standard fashion, with spin axis and ship long axis coincident to each other.

So when the Leonov approached the derelict Discovery, you'd expect that it would be spinning on its long axis.

Instead, the freaking ship is flipping end-over-end. What the frak is going on?

Well, as it turns out, rotation around the roll axis of a long thin object isn't stable. Rotation at 90° to the roll axis is stable.

A long thin object spinning about its roll axis is the object's minimum moment of inertia mode. Windmilling end-over-end is the maximum moment of inertia mode. As it turns out, a long thin object spinning in minimum moment of inertia mode that has any flex to it at all will dissipated a small amount of rotational energy. This will destabilized any rotation that was not in the maximum moment of inertia mode. On general grounds, the body ends up in the spin state that minimizes the kinetic rotational energy for a fixed angular momentum (this being the maximal-inertia axis).

Bottom line is: since the Discover is a long thin object, when the centrifuge braked to a halt causing it to spin on the roll axis, the flex in the ship gradually precessed the spin axis to end-over-end. The movie got it right.

This was actually observed in the real world.

In 1958 (shortly after I was born) the Explorer 1 space probe was launched as part of the International Geophysical Year. The science package was designed by Dr. James Van Allen. The temperature sensors and micrometeorite impact sensor provided mostly uninteresting data. The Geiger radiation counter on the other hand screamed bloody murder at certain parts of the orbit and zero radiation at others. This is now called the Van Allen Radiation Belt and was considered to be one of the outstanding discoveries of the International Geophysical Year. But I digress.

The point was that Explorer 1 was design to spin around the roll axis, but refused to do so. Yep, it precessed to do an end-over-end baton flip in only a single orbit. You may notice the four long flexible antennae, they worked admirably to dissipate the rotational energy. This observation motivated the first further development of the Eulerian theory of rigid body dynamics after nearly 200 years, or so I've been told.

As it turned out a scientist named Ronald Bracewell knew this was going to happen, because galaxies spin the same way. Bracewell called engineers at the Jet Propulsion Laboratory to warn them, but the security people wouldn't let him talk to the engineers.

### 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. 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.

I found some more details in a report Self Erecting Manned Space Laboratory (page 146) by R. Berglund and E. Weber (1962). They went through several options before settling on the above design.

They start off by noting that [a] spin grav space stations need a sizable spin radius or the astronauts are constantly vomiting, and [b] such a radius precludes launching the station assembled in its final form. The images below are never going to come to pass, the report says "However, it is obvious that a vehicle with sufficiently large diameter to permit a moderate level of artificial gravity to be simulated with a low rotational velocity is not capable of being boosted into orbit in one piece because of geometric factors.".

So you are going to have to launch the station not in its final form.

The classic idea was to just launch into orbit girders, plates, welding units, and astronaut construction workers. They would build the station in orbit. This was dismissed as impractical, inefficient, and downright dangerous for the astronauts. And dangerous for NASA, it won't take many astronaut deaths to shut NASA down entirely.

So the next concept is to launch into orbit modular space station bits. This will drastically cut down the construction time, and reduce the danger to the astronauts. Now the problem is trying to find the sweet spot for the module size. The advantage of larger modules is you will shorten construction time since fewer units will be needed to assemble the station. The disadvantage is if they are too large and/or too irregular in shape, the booster cannot transport them into orbit.

But then some brilliant engineer wondered if you could avoid the requirement for constructing the station at all. What if you could deflate the station and inflate it in orbit, or fold it up into something smaller that will fit the booster but unfold like a flower in orbit? This would allow zero construction astronaut danger. You would have a self-erecting space station.

The problem with inflatable space station is [a] equipment cannot be installed prior to launch since the equipment does not deflate, and [b] over long durations meteors will pop the station like a balloon. I will note parenthetically that the second problem is not really a problem. Bigelow Aerospace is developing inflatable space stations in a big way, and flexible walls are actually more resistant to meteorite punctures than rigid walls. Particularly if the flexible walls are made out of bullet-proof Kevlar. Their B330 module has been on the International Space Station since 2016 with nary a leak. But I digress.

The report is about a design by the Langley Research Center which uses both inflatable and foldable concepts to make a hybrid with the best of both. It has six rigid cylindrical sections with equipment already installed, with each section joined by inflatable sections. When folded up it will fit into the payload faring of a Saturn C-5 booster. Once in orbit, it can unfold all by itself with no need for any construction astronauts.

Then there is the problem of the station shape.

The ideal shape is a circle. Sadly this is harder to manufacture, and it is certainly makes it far more difficult to launch. See figure 6, on the right side. It really makes the booster rocket's payload faring bulge out, and creates an aerodynamic buffet during launch.

The less ideal shape is a polygon centrifuge. As shown in the above diagram (and earlier in this section), the amount of gravity is variable and the floor feels like it is inclined. The report suggests using the stepped floor solution as mentioned earlier. Because as figure 9 shows the folded polygon centrifuge is a heck of a lot easier to launch.

The report decide to go with the polygon centrifuge.

The station will have mechanical actuators at each hinge. These will carefully unfold the station into its final form. Note that the hub is rather large. If you look at the right side of figure 9 you will see this is because the hub is at the bottom and has to carry the load of all the other components sitting on top of it.

The station will have a huge internal volume of about 1,700 cubic meters. Which means it can house much more than the original planned 6 person crew. It could easily hold 27 crew, but 21 was set as nominal due to duties and work load in the laboratories. With an expanded crew, a single docking port is not enough. In case of emergency the entire crew will have to be evacuated. Since a single Apollo command module can only hold three crew, the hub will need seven docking ports for seven command modules, so that 21 crew can be evaculated.

The centrifuge is always spinning. The hub is de-spun so as to be stationary while a command module docks/undocks. When astronauts in the hub wish to enter the centrifuge, or vice versa, the hub is spun to match the centrifgue and the hub transfer airlock mates with one of the centrifuge's radial arm tunnels.

As more command modules dock, they will have to be held in a radially symmetric pattern, or the blasted hub will make the entire station wobble when the hub is spun up.

### Polygon Alternative

I found another design for a self-erecting spin gravity station that avoids the weird gravity of the polygon station. A self-erecting tumbling pigeon, as it were.

The example in the diagram above uses the same module dimensions as the polygon station above: 22.9 meters long by 3 meter in diameter. Seven modules, including the one in the center used as a hub. Hanging off the hub are two arms, each with three modules. In each arm, one module is just a truss, the two on the end are pressurized habitat modules. The entire thing is tied together with tethers.

• Centrifugal gravity does not vary appreciable across each floor.
• No "stepped" floor required.
• 100% usable floor space, since floors are perpendicular to long axis instead of parallel like the polygon station.

Disadvantage is that the centrifugal gravity varies between floors. But that is common with many designs. At 3RPMs, the bottom floor (47.9 meters from spin axis) will have 0.48 g, 0.25 g at the top (25.0 meters from spin axis), and a Mars-like 0.37 g in the middle (36.5 meters from spin axis). Centrifugal gravity is reduced by 0.025 g for each 2.5 meters closer to the spin axis.

The truss sections will have low but not zero gee, and can be used to store equipment and life support.

### Unexpected Spin

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.

## Spin Grav Types

### Dependent Centrifuge

#### 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 more modern term is "baton" mode, referring to baton twirling.

The idea is to increase Cl. If you do a conventional spin on the long axis then Cl is the relatively tiny width of the ship, leading to either pathetically low gravity or the crew constantly vomiting due to spin nausea.

But if you use the clever Tumbling Pigeon method, you spin on the short axis and Cl is the entire freaking length of the ship. Then you can easily have a high spin gravity with no spin nausea.

There is a drawback, of course. If the crew spaces are located in the "top" of the ship and the engines are in the "bottom", you have a problem. When you enter tumbling pigeon mode, the directions of "up" and "down" in the crew spaces will reverse. The floor will become the ceiling, with all the problems that entails.

Exception: Michael Hutson points out that Waterskiing spacecraft are immune to the problem. The orientation of "up" and "down" in the crew compartment stays the same, because the crew compartment is in the "bottom" of the ship.

There were a couple of real-world designs usings the tumbling pigeon technique (e.g., Mars NEP with Artificial Gravity and Stuhlinger Ion Rocket). In the designs a dependent centrifuge would not provide a long enough Cl unless the habitats were put on long radial arms. This increases the structural mass and cuts into the payload mass. By using the tumbling pigeon arrangement, the ship's spine does double duty as framework and as radial arms. No extra structural mass needed.

#### 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."

Basically it is a tumbling pigeon with cables in the middle instead of spacecraft spine.

### 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.

#### Canfield Joint

One of the nagging problems with an independent centrifuge is trying to transfer power and/or fluids across the hub. You cannot just put a cable or hose across because the spin will just keep twisting it until it snaps. Many designs try to use slip-rings (to transmit power) and rotary unions (to transmit fluids) but these are maintenance horror-shows and have limited capacity. Try sending megawatts over a slip ring and see how long it lasts. And if you are trying to send multiple fluid types (e.g, drinking water and sewage) the problem multiplies.

One possible solution is to use a Canfield Joint. It can move a linkage over 360° without twisting any number of hoses and cables. Watch the video, especially the part about the solar panels. Note that while the spacecraft is spinning, the orientation of the solar panels will be constantly changing but they will always be perpendicular to the sun. The same will apply to an array of ion drive rockets, the orientation will constantly change but they will always be aimed at the mandated thrust axis.

#### 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. Whether they are part of an independent or dependant centrifuge, the gimbaled centrifuge is adding an additional set of gearing, machinery, and points of failure.

In addition, they all suffer from the sloped floor problem inherent in the Polygon Centrifuge. The floor will seem like it has a series of hills and valleys. The only choices the ship designers will have is will the floor seem normal under centrifugal gravity and hilly under thrust, or vice versa?

A third problem is the variable gravity. Remember that the effective gravity depends upon the floor's distance from the spin axis. So spacecraft designers tend to make the gravity section only one or two floors "tall". The more floors, the more drastic the gravity difference between the top floor and the bottom floor.

The problem happens when spacecraft designers try to deal with the polygon centrifuge slope problem by dividing up the centrifuge into a series of narrow segments instead of one big ring. The idea is that in a narrow segment it is not quite so obvious that the floor slopes. The problem is that since the segments are narrow, in order to get the same ground area as a continuous ring you will be forced to stack multiple segments. Then the variable gravity problem rears its ugly head. Examples of this arrangement include the Pilgrim Observer and Dream Pod 9.

##### 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.

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". 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 tall narrow 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, and are subject to the variable gravity problem. It would be nice if you could somehow rotate the orientation of a full 360° 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 it still suffers from the sloped floor problem. Because that problem is addressed by using tall narrow slabs for the centrifuge. Which this design was trying to avoid.

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 solution I've manage to think up involve dynamically altering the contour of the floor, which is an engineering nightmare.

## Spin Power

Like everything else, spinning a centrifuge up or down will require power. Most NASA designs use attitude jets at the rim of the centrifuge regardless of whether it is a dependent or independent centrifuge. But some fancier designs feature an independent centrifuge designed like a titanic electric motor, with the spinning centrifuge as the rotor and the stationary ship core as stator. If you want to spin a dependent centrifuge using electricity, use a reaction wheel.

The advantage of attitude jets is they are mechanically simpler than reaction wheels or giant motors. The disadvantage is that jet fuel gets used up and more will have to be imported.

The advantage of reaction wheels is they use no jet fuel. When the wheel is braked to a halt, the spin is converted into electricity and stored in batteries (with some conversion losses). To spin up the wheel you simply tap the power in the batteries, and top off the losses with some juice from the stations power plant.

The disadvantage of reaction wheels is they are much more complicated, and have far more points-of-failure compared to attitude jets.

### Power Demands

How much power is required to spin up or spin down the centrifuge? Well, that depends upon the centrifuge's mass, movement of inertia, and rotation rate.

First you find a Moment of Inertia equation that approximates your centrifuge:

• Wheel type space station or wheel type independent centrifuge: Torus
• Balanced Tumbling Pigeon: Rod about center
• Unbalanced Tumbling Pigeon: Rod about end (if engine is massive)
• Dependent centrifuge: Solid cylinder or disc, symmetry axis
• Gimbaled centrifuge: I'm still trying to find an equation for that

Use the appropriate equation, plug in the centrifuge mass and dimension(s), and calculate the Moment of Inertia I in kilogram-square meters (kg⋅m2).

Now take the rotation rate Cr (rotations per minute) and convert it to rotation rate Crrad (radians per second)

Now calculate the Torque τ in Newton-meters (N⋅m).

This is the amount of Torque that must be imparted to that particular centrifuge to spin it up to the desired rate, or spin it down from that rate to stationary.

Assume we are spinning up by using attitude jets. Say we have a tumbling pigeon, and are using one jet on the ship's fore end (the nose) at 90° to the ship's long axis and a second jet on the ship's aft end (the tail with the rocket engines), at 90° in the opposite direction of the first jet. There are two jets, so each is responsible for τ / 2 worth of torque.

τfraction = τ / NumAttitudeJets

How many Newtons will each jet have to thrust in order to impart the required Torque? Well, the jets are acting like a class 2 lever. This means the farther the jets are from the spin axis, the fewer the Newtons they will have to thrust to create the Torque.

If the centrifuge is a wheel station or independent centrifuge, the attitude jets will be mounted on the wheel's rim, so LeverDist will be the wheel radius.

SingleJetThrust = τfraction / LeverDist

Now, I am a little fuzzy on this, but I'm pretty sure that is the amount of thrust required to produced the desired spin with a one-second burn. Meaning if you used attitude jets with only half that thrust, it would take two seconds to produce the spin. One-third thrust would take three seconds, and so on.

### Spin Power Generation

And a couple of science fiction authors realized that the only difference between an electric motor and an electric generator is which side the power is applied to, the mechanism is pretty much the same. Input electricity, the output is mechanical energy, and you can call the device a "motor". But if you take the same device, input mechanical energy, receive electricity as output, then you can call it a "generator".

Meaning if you take a motor and plug it into the electrical wall socket, the rotor spins. But if you manually spin the rotor, electricity comes out of the motor's wires.

This sounds like an academic point. Until that fine day when your ship is far from help and the power plant unexpectedly fails…

## Asteroid Spin Grav

An asteroid colony or asteroid mine might have the quality of life increased if it can be equipped with spin gravity. The classic technique is blowing an asteroid bubble, it is a pity that it probably won't work.

The safe way is digging out a cylindrical hole for the colony/mine inside the asteroid and spinning the asteroid.

I found an interesting document Stability Of A Rotating Asteroid Housing A Space Station where they focus on asteroid in the size range of 100-500 meters. They try to create a mathematical model to figure out how big the hole and how fast the spin you can get away with, before the rocky asteroid fractures into high-speed meteors.

## Making Do Without

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.

### 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.

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. One episode also showed that if a person wearing mag boots is shot and killed, they do not fall down. They sort of creepily float in place, attached to the deck by their feet.

In the movie 2001 A Space Odyssey the stewardess wore velcro footies to walk on the velcro floor.

In Robert Forward's Rocheworld, the space marines use 'stiction boots. In Poul Anderson's Tau Zero, they have bondsole shoes.

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.

## Atomic Rockets notices

This week's featured addition is SPIN POLARIZATION FOR FUSION PROPULSION

This week's featured addition is INsTAR

This week's featured addition is NTR ALTERNATIVES TO LIQUID HYDROGEN