Artificial 1g Gravity on Mars vs in Space

martienne · 2017-04-02 12:40:03

Hi all, I'm really struggling to get my head around the finer details of how artificial gravity works.
For space, is there any good explanation with an illustration or example?

And what would it take on Mars, to simulate Earth gravity? I assume it would be very energy demanding, but what would be the most practical way to do it. Let's say you wanted an area the size of a football/soccer field to have Earth gravity, how would you do it?

SpaceNut · 2017-04-02 13:21:15

A structure on mars would be simular to this concept... Its a ride at the fair we would make it larger...

RobertDyck · 2017-04-02 13:47:03

Are you familiar with vector math? I took it in grade 12 physics. I understand not everyone gets the same curriculum in high school. When I worked at Micropilot in 2003, just outside Winnipeg, one co-worker was an immigrant from Ukraine. He took aerospace engineering at a university in Moscow, Russia. So it's no surprise that he had dramatically different education. I went to the high school that had a reputation for the best science curriculum in the city. Our grade 11 physics teachers said we would learn everything in first year university physics, and some of second year. What really surprised this immigrant from Ukraine was when I said one exercise in grade 11 physics in 1978-1979 was to design a phased array antenna for a fictional radio station. The exercise included a map of Manitoba and North Dakota, and this fictional radio station wanted maximum coverage over small towns in southern Manitoba, with minimum transmission into North Dakota. We had to map reinforcement and cancellation nodes, map exact signal strength, and show exactly where our proposed design would have poor or no radio reception. Our exercise even required us to document exactly how many people lived in the poor reception nodes.

Because my high school scheduled grade 12 physics in the same time slot as grade 12 computer science, I completed high school one course short. I took my last high school course at the same time as 4 out of 5 courses for first year university. The University of Winnipeg let me do that, they had a high school (collegiate) in one building on their campus. So technically I graduated high school from the University of Winnipeg Collegiate. That high school course taught at University covered vector math.

To design for Earth gravity, you need rotating cone. The inside surface of the cone will have simulated Earth gravity. The axis of rotation will be perpendicular to the surface of Mars, which means centrifugal force will be outward, parallel to Mars surface. The vector math is to add the centrifugal force from the centrifuge, with gravity from Mars. Or to design this, do the reverse calculation. To achieve total acceleration equal to Earth gravity, you must add Mars gravity to how much centrifugal force?

Caution. The total acceleration will be an angle; that's why the centrifuge must be a cone. So the inside surface of the cone "feels" level. However, the portion of the cone with smaller diameter will have less centrifugal force than the large end (top) of cone. The top will have more acceleration. To minimize difference, the cone should be relatively narrow. Viewed from outside, that means less tall than it is wide.

SpaceNut · 2017-04-02 14:15:17

Here is what RobertDyck is talking about Centrifugal Force vs Centripetal Force Formula Fc = mv2/r

Both forces are calculated using the same formula:

F = ma_c = \frac{m v^2}{r}

where ac is the centripetal acceleration, m is the mass of the object, moving at velocity v along a path with radius of curvature r.

RobertDyck · 2017-04-02 14:49:36

Now do vector math. It's just a triangle. Start with some statistics. The website SolarViews has numbers in easy to use form.
Earth - Equatorial surface gravity (m/sec^2) 9.78
I like to express that in a form engineers and mathematicians are used to. If you use Windows, click "Programs" or "All Programs", then "Accessories", then "System Tools", and finally "Character Map". This shows characters available. Click the small raised digit "2" for "squared", then click the "Select" button, then click "Copy". This will put the "square" symbol on the clip board. You can then use Ctrl-V to paste in "Quick reply" for NewMars. Putting it together:
Earth equatorial surface gravity = 9.78 m/s²

Mars - Equatorial surface gravity 3.72 m/s²

So the goal is to get 9.78 m/s². In vector math, that's the hypotenuse of a right triangle. One of the sides of the triangle is Mars gravity = 3.72 m/s². The goal is to get the other size, which is centrifugal force. (Centripetal force points toward the centre of rotation; centrifugal force points away from the centre.)
Basic grade school math will tell you A² + B² = C². Where "A" is one side, "B" is the other side, and "C" is the hypotenuse. So to calculate required centrifugal force: Square root ( C² - A² ) = Sqrt( 9.78² - 3.72² ) = Sqrt( 95.6484 - 13.8384 ) = Sqrt( 81.81 ) = 9.045 m/s²

Ok, that's almost all acceleration due to centrifugal force. Mar gravity provides very little.

Now to calculate angle. It's trigonometry. You have all three sides, expressed as acceleration. You want the "floor" of the centrifuge to feel level. In the image of the amusement park ride that SpaceNut posted above, the wall that people have their back to will be the "floor" when it's rotating. So what's that angle? Hypotenuse is 9.78 m/s², adjacent side is 3.72 m/s², angle is inverse cosin( 3.72 / 9.78 ) = 67.6435°. That's the angle above ground level. Or the angle from vertical is 90 - 67.6435 = 22.3565°.

But the floor will not be a flat cone, it will be curved. That's the angle where artificial gravity is exactly Earth gravity. The portion of the cone closer to the centre of rotation is at people's feet in the amusement park ride. Centrifugal force is less there, greater at people's head. So the "wall" they have their back to will be the floor when it's rotating. That will be concave.

martienne · 2017-04-02 15:07:29

Great explanations! Do you think something like that could be designed so it's non-intrusive. I.e. so that somebody on Mars enters this 1 g gravity room and it feels exactly like they are in a normal room on Earth?

Would it be possible to get in and out of the Earth Gravity room from normal Mars gravity, while the room is operational> Or would you have to turn the gravity (i.e. spin) off to leave the room?

In that "Gravatron" ride from the picture - you couldn't walk around, could you? You'd be constantly pressed towards whatever part of the structure it is that's moving. I'm probably one of very few people who have never been in a ride like that at a tivoli. I never liked those spinning rides.

Last edited by martienne (2017-04-02 15:12:28)

SpaceNut · 2017-04-02 15:26:19

The larger that more possible it is but with distance we need to alter the spin ratio as well... The only time I think man really needs to be spinning for long periods of time is while we sleep and the gravitor would be the concept to make use of. To wake up just slowly spin its speed down which is the same for when we ant to go to sleep as well to enter to which we would then speed it back up.
The question we all have had is there any benefit to mars partial gravity or do we really need earths full gravity...

RobertDyck · 2017-04-02 15:37:56

Current TV show "The Expanse" had a scene depicting Mars marines training on Mars in a centrifuge providing Earth gravity. They were running. I wish I could find a clip of that scene. It appeared as a brief flash in Season 2; I've been trying to find the scene.

RobertDyck · 2017-04-02 15:58:10

Have you ever had a meal in a rotating restaurant? The elevator is near centre of rotation. When you get off the elevator, the floor near the elevator does not move. Then step onto the moving floor. The moving floor with tables and chairs and windows is on wheels. A motor constantly drives the restaurant slowly. Over the course of your meal you get a 360° view of the city. I've had a meal at one in Niagara Falls, Vancouver, and Manhattan. A large centrifuge on Mars would work like that. But the floor would rotate faster. Once on the rotating floor, either a ladder or staircase would descend to the outer ring. The farther you step from the centre of rotation, the stronger centrifugal force will be.

Here's an image from the movie "2001 A Space Odyssey". It's supposed to be the interplanetary spaceship Discovery, so there is no Mars gravity.

This is a view of the set where they filmed these scenes. You can see it actually rotated. It wasn't a real centrifuge, it was a giant hamster wheel.

And from the same movie, inside "Space Station V". This is supposed to be a station, so much larger. If you look carefully, you can see the corridor curves up in the background.

Last edited by RobertDyck (2017-04-02 22:39:39)

GW Johnson · 2017-04-02 16:14:56

Just a a guide you can proportionally scale: a 56 m radius at 4 rpm rotation speed is 1 full gee of "centrifugal force" ("centripetal acceleration" for the purists). Effectively, artificial gravity is proportional to radius, and to rotation rate squared. Half the radius at the same speed is half the gravity. Half the speed at the same radius is a quarter the gravity. That's in zero gee in space.

Then on the moon or Mars, you add that amount of effective artificial gravity as a vector 90 degrees away (vectorially) to the local "real" gravity. The resultant of those vectors is what you feel as gravity.

Hope that helps.

GW

Last edited by GW Johnson (2017-04-02 16:19:08)

martienne · 2017-04-02 18:49:09

Thanks for the super helpful pictures and examples....
So it doesn't need to spin amazingly fast then? Or do you work out the required speed based on size, local gravity and desired gravity?

And the person would only feel completely normal as long as he stayed within a fairly limited area of the whole chamber + leaving the room while it's operational... Or could they leave easily through the nave?

elderflower · 2017-04-03 05:34:54

Do we need this on Mars?
I think we will only need it to build up strength for the return to earth, so artificial gravity might only be needed in space for 5 or 6 months. Other than that the exercise regime developed for the ISS seems sufficient.
For those contemplating prolonged stays on the moon, it might be necessary to include a rotating hab section as you don't get 6 months to rebuild when coming back.

louis · 2017-04-03 10:21:43

Yes that's the big question.

There are related questions - if we wore well designed lead (or similar) padded suits and shoes on Mars that were 60% of our body weight, would we actually get the benefits of 1G? Or are there micro-gravity effects that affect cell function in more subtle ways?

I am fairly confident myself that humans will be able to survive, in reasonable condition, a 2 year stint on Mars, together with the two transits, as long as they wear the added-weight suits on Mars, engage in the full exercise programme while in transit and take the requisite space medicines. But there's only one way to find out for sure...

The main problem I foresee is people coming back with severely depleted immune systems. I think there may be an argument for deliberately infecting the colonists with relatively mild pathogens at regular intervals throughout the expedition in order to keep the immune system exercised.

SpaceNut wrote:

The larger that more possible it is but with distance we need to alter the spin ratio as well... The only time I think man really needs to be spinning for long periods of time is while we sleep and the gravitor would be the concept to make use of. To wake up just slowly spin its speed down which is the same for when we ant to go to sleep as well to enter to which we would then speed it back up.
The question we all have had is there any benefit to mars partial gravity or do we really need earths full gravity...

SpaceNut · 2017-04-03 17:34:04

Well make the suit with extra pockets to hold the extra weigh but that said we will use insitu materials as its to costly to bring it from earth....

RobertDyck · 2017-04-03 18:34:02

Settlers will live just fine on Mars. They will develop weaker muscles, because they aren't needed. And weaker bones. The current TV show "The Expanse" is about a time when the solar system is settled, but technology to travel to stars does not yet exist. They claim the UN runs all of Earth, and Mars has one government. The point is they claim Mars marines train in Earth gravity simulators, because they may be called upon to invade Earth. The show is described as "Game of Thrones in space"; again something I want to avoid.

A simulator like this could be built. It would be relatively small, and expensive. It would only be used to condition a Mars settler in preparation for a trip to Earth.

martienne · 2017-04-03 18:45:14

RobertDyck wrote:

A simulator like this could be built. It would be relatively small, and expensive. It would only be used to condition a Mars settler in preparation for a trip to Earth.

Thanks Rob! Yes, I was more interested in the basic how-to of it, than whether it's needed. It doesn't need that much imagination to think of future scenarios where something like that might be desirable and
Your earlier examples and this paragraph sums it up for me.

Just one thing: Would you be able to leave it while the gravity is operational? Or does the spinning mean it's impossible to leave the room while it's moving?
In terms of energy - could it run off solar power or would it need something more heavy duty?

The Expanse is awesome as a series, I like the tech and the politics - but not some of the unrealistic or annoying politically correct stuff they added. I think I missed that shot of the Mars Marines training for Earth gravity. I think there are some gaps to the logic though; like how do the Mars and Asteroid belt societies pay for themselves; that would require space travel suddenly being dead cheap - the author never explains how that happens.

Last edited by martienne (2017-04-03 18:47:28)

SpaceNut · 2017-04-03 19:28:48

You would stop the spinning in order to exit or enter as needed.

The trouble is the unknown for how long we need to be within it? If its more than a 8 hr time we will be looking at what time of day do we want to use it as solar means a doubling of size to compensate for the power needed for batteries to make use of it during the night.

louis · 2017-04-04 03:26:00

Yes, that makes a lot of sense, although for the first mission, perhaps they would go with pre-prepared integral suits.

SpaceNut wrote:

Well make the suit with extra pockets to hold the extra weigh but that said we will use insitu materials as its to costly to bring it from earth....

louis · 2017-04-04 03:27:46

It could be powered by methane, produced by PV power during sol-light.

SpaceNut wrote:

You would stop the spinning in order to exit or enter as needed.
The trouble is the unknown for how long we need to be within it? If its more than a 8 hr time we will be looking at what time of day do we want to use it as solar means a doubling of size to compensate for the power needed for batteries to make use of it during the night.

Terraformer · 2017-04-04 04:43:28

To get out, you would walk to the centre and take the lift. Maybe there would be a ring between them that can be used to match spin and make the transition easier, if needed.

Spaniard · 2017-04-04 05:33:21

louis wrote:

Yes, that makes a lot of sense, although for the first mission, perhaps they would go with pre-prepared integral suits.

SpaceNut wrote:
Well make the suit with extra pockets to hold the extra weigh but that said we will use insitu materials as its to costly to bring it from earth....

It's probably has a extra weight than nothing on Mars, but it's not the same that gravity. The weight through this system is external pressure in some places in the body, while gravity acts equals in all points including internal fluid like blood.

At long term, rotatory buildings are a bood idea.

I think that a good structure is cilindrical, while the floor is perceived as a stair or a slope. It allows more "horizontal space" as we are habituated. More like soft cones truncated and stacked one over another.

And big radius. Not all the building is neccesary, only the ring. If the weight of the structure is too much it can be attached to a stacked external rings (viewed as underground from a person inside the rotatory building).
As we can stack in the same level as the length of the building, it would allow bigger buildings.

Probably walls would be a good idea to allow stop anything inside the building and don't fall from a high altitude. Shelves on the Mars floor direction.

It could levitate like a magnetic train, so total energy lost normally is small.

Tom Kalbfus · 2017-04-04 06:00:53

martienne wrote:

Thanks for the super helpful pictures and examples....
So it doesn't need to spin amazingly fast then? Or do you work out the required speed based on size, local gravity and desired gravity?
And the person would only feel completely normal as long as he stayed within a fairly limited area of the whole chamber + leaving the room while it's operational... Or could they leave easily through the nave?

The larger your spin radius the higher the tangential velocity needs to be to produce 1-g but also the lower the spin rate. A large spin radius is less likely to produce nausea and is less distinguishable from natural gravity than a small spin radius. It is easier to implement small spin radiuses on a world's surface, but ultimately, the spin radius can eventually be larger around a gravitational body than we can in free space. for example if we can get close to Jupiter, we can theoretically build a ring that is slightly larger than Jupiter's atmosphere, Jupiter is by the way 43,441 miles (69,911 km) in radius, we could not build a ring-shaped space colony with a radius of 43,700 miles (70,328 km) for instance, but we can around Jupiter because Jupiter has a gravity 2.4 times that of Earth so for every 2.4 kilograms of the ring, we need only 1 kilogram of counterweight to prevent the ring from breaking apart, we would need to spin the ring at a rate to produce 1 more g of gravity than Jupiter has to produce an outward force of 1-g. We would need a spin velocity of 48,424 meters per second and a rotation rate of 152 minutes per rotation, it probably makes more sense to have an outward rotation force of 1-g rather than an inward residual gravity of 1-g, because then you would need 2.4 kilograms of rotational mass to support every 1 kilogram of counter weight. Also the later only works with planets that have gravity higher than Earths, the former can be done with the Moon or Mars. With the Moon for instance, you would need about 6 kilograms of counter weight for every kilogram of the ring, this is not taking into account the actual tensile strength of the material. In free space, you are limited by the tensile strength of the material you are spinning as there is very little inward force of gravity to work with. You could even do this with Ceres but you would need about 20 kilograms of counterweight for every 1 kilogram's mass of the ring.

GW Johnson · 2017-04-04 18:58:45

Staying on Mars is followed by a multi-month journey back to Earth. If your vehicle during the return journey is equipped with artificial gravity at something near a 1 gee level, you have plenty of time to recover enough fitness to survive a 12-15 gee emergency Earth reentry at the end of your mission.

The moon is different: it only takes 3 days to come home, to an 11 gee re-entry. Fitness to survive the return home is actually much more of an issue with the moon than it is Mars. The exercise regimen they use at ISS is such that returning astronauts are fit to survive a 4-gee entry from Earth orbit. So either (1) we find a way to stay fit for 11 gees on the moon, or (2) we drastically shorten allowable stays on the moon.

GW

louis · 2017-04-04 20:23:08

True, but we will already be getting 38% gravity won't we? So the issue, is whether that, combined with the artificial weights, would be enough to keep us reasonably healthy.

Certainly sleep centrifuges may prove necessary or desirable for longer stays. We simply don't know yet.

Spaniard wrote:

louis wrote:
Yes, that makes a lot of sense, although for the first mission, perhaps they would go with pre-prepared integral suits.

SpaceNut wrote:
Well make the suit with extra pockets to hold the extra weigh but that said we will use insitu materials as its to costly to bring it from earth....
It's probably has a extra weight than nothing on Mars, but it's not the same that gravity. The weight through this system is external pressure in some places in the body, while gravity acts equals in all points including internal fluid like blood.
At long term, rotatory buildings are a bood idea.
I think that a good structure is cilindrical, while the floor is perceived as a stair or a slope. It allows more "horizontal space" as we are habituated. More like soft cones truncated and stacked one over another.
And big radius. Not all the building is neccesary, only the ring. If the weight of the structure is too much it can be attached to a stacked external rings (viewed as underground from a person inside the rotatory building).
As we can stack in the same level as the length of the building, it would allow bigger buildings.
Probably walls would be a good idea to allow stop anything inside the building and don't fall from a high altitude. Shelves on the Mars floor direction.
It could levitate like a magnetic train, so total energy lost normally is small.

RobertDyck · 2017-04-04 21:50:22

louis wrote:

True, but we will already be getting 38% gravity won't we? So the issue, is whether that, combined with the artificial weights, would be enough to keep us reasonably healthy.
Certainly sleep centrifuges may prove necessary or desirable for longer stays. We simply don't know yet.

I doubt very much that we will need anything more than Mars gravity. That was supposed to be confirmed by the centrifuge module on ISS. But even that centrifuge was only large enough for animal studies, not humans. But laboratory mice can be dissected.

Again, my premise is that gravity causes convection and other currents with cells, as well as movement of solids within the liquid of cells. That should negate most of the zero-G effects, leaving only adaptation to lower stress from lower gravity. This can be confirmed by said animal studies in a centrifuge on ISS. If so, then as GW Johnson said, all we need is artificial gravity on the return trip back to Earth. That's enough, nothing more.

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Artificial 1g Gravity on Mars vs in Space

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