Artificial gravity meeting zero gravity

[icez]

A little puzzle that's been in my mind for a while and I figured I would ask, in case someone a little more knowledgeable could shed some light on it.

Assuming one had a spaceship formed by two "hoops," one inside the other. If one of the hoops rotated at a velocity high enough to provide a sense of artificial gravity, and the other hoop remained stationary. A ladder or stairway would provide access between each hoops from the inside. If someone was inside the moving hoop, with gravity and all, then went into the stationary hoop, what would happen?

I'm assuming this would take place in a low gravity environment. However, I'm wondering if the individual would start floating as he made his or her way down, or right at the moment they stepped off the ladder? Would someone in the stationary hoop floating right over the stairway suddenly crash on it as it moved under him?

Here's a not so good drawing, if it helps any.
[PLAIN]http://img203.imageshack.us/img203/6279/stairship.png

Thanks!

 

[russ_watters]

Which is stationary and which is rotating?

 

[DaveC426913]

The first thing you need to recognize is that there is no artificial gravity in a spinning space station. All there is is inertia - moving in a straight line, tangential to the perimeter of the hoop.

That movement comes from the occupant having been given a push by touching a surface moving relative to him (or air resistance).

No touch = no push
No push = no tangential movement
No tangential movement = no artificial gravity

In summary, the occupant will be weightless until
1] he physically touches a surface moving relative to him imparting some tangential movement
AND THEN
2] his tangential movement subsequently causes him to bump into the wall again. It is THIS motion-and-bump that he experiences as an apparent force pulling him to the floor.


He can float weightless next to a space station floor whizzing by at 100mph forever. It is when he reaches out and makes contact with the wall (causing him to pick up some motion relative to the space station as a whole) that he begins to experience artificial gravity. And the strength of the AG wil be proportional to how much motion he picks up. Just grazing it with his fingers won't do much - at first, but it's enough that he will slowly and inevitably speed up and come to rest moving at 100mph.

 

[AJ Bentley]

he will slowly and inevitably speed up and come to rest moving at 100mph.

Most of him will.
There'd probably be a few gobs and splatters floating around.

 

[icez]

That actually makes a lot of sense, thanks for the clarification!

 

[brainstorm]

interesting. So if the person is moving at 100mph on the outer wall of the space station, how do they return to weightlessness relative to the moving floor? If they accelerate to 100mph in the opposite direction as the outer wall, they become weightless? What if they accelerate to 100mph in the same direction the wall is moving? Do they become heavier (i.e. gain more momentum)?

So, if I understand this right and there was a very large hollow cylindrical space station, a person wanting to travel hundreds of miles would just need to accelerate to the speed of the station's momentum from the ground and could then fly without gravity to the other side where it would have to accelerate up to speed again to land?

 

[DaveC426913]

interesting. So if the person is moving at 100mph on the outer wall of the space station, how do they return to weightlessness relative to the moving floor? If they accelerate to 100mph in the opposite direction as the outer wall, they become weightless? What if they accelerate to 100mph in the same direction the wall is moving? Do they become heavier (i.e. gain more momentum)?

Yes on both.

One of the (many) tricky things about AG rotating spaces tations is that moving to spinward will make you feel heavier and moving to antispinward will make you lighter. Move too fast to antispinward and you will become so light that you will have difficulty getting traction, you'll go more "up" than "along".

So, if I understand this right and there was a very large hollow cylindrical space station, a person wanting to travel hundreds of miles would just need to accelerate to the speed of the station's momentum from the ground and could then fly without gravity to the other side where it would have to accelerate up to speed again to land?

Well, yes. It's not quite as simple as that, but yes.

For one, air will be moving along with the rotation, and will work to keep you moving along with the station. At its worst, you'd be battling a 100mph wind to keep weightless, so...

 

[brainstorm]

For one, air will be moving along with the rotation, and will work to keep you moving along with the station. At its worst, you'd be battling a 100mph wind to keep weightless, so...

So as you're accelerating in the antispin direction, your weight is approaching zero while your lift is increasing toward whatever it would be at 100mph. At some point in between 0 and 100mph, you would reach some kind of ideal combination of lift and weight and would take off stably, right? Then could you fly more or less straight up (into the headwind) toward your destination and just glide with the wind back to a reasonable landing speed?

I think I'm just saying what you did in a wordier way, but I wonder how the reduced weight would interact with the lift and what kind of trajectory the plane would have to take.

 

[DaveC426913]

So as you're accelerating in the antispin direction, your weight is approaching zero while your lift is increasing toward whatever it would be at 100mph. At some point in between 0 and 100mph, you would reach some kind of ideal combination of lift and weight and would take off stably, right? Then could you fly more or less straight up (into the headwind) toward your destination and just glide with the wind back to a reasonable landing speed?

I think I'm just saying what you did in a wordier way, but I wonder how the reduced weight would interact with the lift and what kind of trajectory the plane would have to take.

There's no lift. All there is is you trying to run and resulting in pushing off the ground.


Note that you cannot run at 100mph. To achieve weightless, you'll need to be in a space staiton whose rotational speed does not exceed your running speed.

 

[brainstorm]

There's no lift. All there is is you trying to run and resulting in pushing off the ground.


Note that you cannot run at 100mph. To achieve weightless, you'll need to be in a space staiton whose rotational speed does not exceed your running speed.

In my example the space station was hundreds of miles across and there was a plane accelerating in the anti-spin direction simultaneously losing weight and gaining lift. In your example, the space station seems to be smaller and slow enough to achieve weightlessness on foot. I was interested in the dynamics of lift vs. weight in a plane flying counter the spin direction.

 

[DaveC426913]

In my example the space station was hundreds of miles across and there was a plane accelerating in the anti-spin direction simultaneously losing weight and gaining lift. In your example, the space station seems to be smaller and slow enough to achieve weightlessness on foot. I was interested in the dynamics of lift vs. weight in a plane flying counter the spin direction.

Right. I saw that after-the-fact.

But you're looking at the least interesting case. You're still building a large plane that has to accelerate to 100mph and use lifting surface to get off the ground. Why not take advantage of the unique quirks of the AG? It's much more fun.

In a nutshell, in a large enough space station, your airplane would take off just like a plane on a planet would, but would experience an excess of lift (lift it would not need). In fact, the lift would have to be coutnered by control surfaces to get the plane to fly straight instead of rising too rapidly.

Moreover, the plane would now have no use for its wings (since there's no gravity force), and would become simply a propellor-powered missile, its direction of motion determined by the propellor's axis. Control surfaces would simply redirect the long-axis of the craft.

 

[brainstorm]

Right. I saw that after-the-fact.

But you're looking at the least interesting case. You're still building a large plane that has to accelerate to 100mph and use lifting surface to get off the ground. Why not take advantage of the unique quirks of the AG? It's much more fun.

In a nutshell, in a large enough space station, your airplane would take off just like a plane on a planet would, but would experience an excess of lift (lift it would not need). In fact, the lift would have to be coutnered by control surfaces to get the plane to fly straight instead of rising too rapidly.

Moreover, the plane would now have no use for its wings (since there's no gravity force), and would become simply a propellor-powered missile, its direction of motion determined by the propellor's axis. Control surfaces would simply redirect the long-axis of the craft.

I think you're assuming either 100mph and weightlessness or 0mph and full AG. What I'm looking at is where the plane accelerate anti-spinward, which decreases its weight while increasing its lift. As you said, the air inside the space station basically rotates along with the "ground" so it's not possible to go in the anti-spin direction without attaining lift. However, as you say if you achieve 100mph the plane would become weightless and turn into a propellor-powered airborne torpedo.

So the interesting thing would be to plot a course for the plane that accelerates to, say, 50mph where it still maintains weight due to the rotation of the station, but the weight is reduced while lift is present. Then, once it is airborne would it then make sense to go ahead and accelerate to full weightlessness or should the plane operate at <100mph to remain sub-weightless?

 

[DaveC426913]

I think you're assuming either 100mph and weightlessness or 0mph and full AG. What I'm looking at is where the plane accelerate anti-spinward, which decreases its weight while increasing its lift. As you said, the air inside the space station basically rotates along with the "ground" so it's not possible to go in the anti-spin direction without attaining lift. However, as you say if you achieve 100mph the plane would become weightless and turn into a propellor-powered airborne torpedo.

So the interesting thing would be to plot a course for the plane that accelerates to, say, 50mph where it still maintains weight due to the rotation of the station, but the weight is reduced while lift is present. Then, once it is airborne would it then make sense to go ahead and accelerate to full weightlessness or should the plane operate at <100mph to remain sub-weightless?

:shrug:
OK, I just don't see much interesting about that is all. I know how planes work. This is just more of the same.

What I find more interesting is the longtime dream of humanity coming to life - a person flying by muscle-power alone.

 

[brainstorm]

:shrug:
OK, I just don't see much interesting about that is all. I know how planes work. This is just more of the same.

What I find more interesting is the longtime dream of humanity coming to life - a person flying by muscle-power alone.

Ok, well how fast would the station have to be rotating to produce 1G? I'm sure you could make a space station small enough to generate 1G with relatively low speed. In that case, you could lose lots of weight by running antispinward but how would you propel yourself once you leave the ground?

 

[DaveC426913]

I'm sure you could make a space station small enough to generate 1G with relatively low speed.

Other way around.
For 1G, slow speed requires a big station. You want a small station, speed must be high.

 

[brainstorm]

Other way around.
For 1G, slow speed requires a big station. You want a small station, speed must be high.

Why are the speeds actually even different? Isn't the G-force just a product of the momentum of the objects inside the station. So shouldn't any object move with 1G of force if it is accelerating at a given rate?

 

[DaveC426913]

Why are the speeds actually even different? Isn't the G-force just a product of the momentum of the objects inside the station. So shouldn't any object move with 1G of force if it is accelerating at a given rate?

The object is not accelerating. The object is traveling in a straight line (tangential to the space station's rim). It is the space station that curves up toward the object. It is this floor-coming-toward-object that is (mis)interpreted as an apparent force pulling the object toward the floor.


Shoot, I am now no longer sure that this is correct:

I'm sure you could make a space station small enough to generate 1G with relatively low speed.

Other way around.
For 1G, slow speed requires a big station. You want a small station, speed must be high.

Here're some numbers:

Ok, well how fast would the station have to be rotating to produce 1G?

 

[cjameshuff]

Other way around.
For 1G, slow speed requires a big station. You want a small station, speed must be high.

The force is proportional to the radius and to the square of angular velocity, but tangential velocity is directly proportional to both. If you quadruple the radius, you must halve the rotation rate, which still gives you double the linear velocity. Larger stations require lower rotation rates, but higher tangential velocities. (As the radius of curvature increases, the speed along that curve must increase to maintain the same acceleration.) And in this case, it seems to be that tangential velocity that's of interest, not the rotation rate.

 

[DaveC426913]

The force is proportional to the radius and to the square of angular velocity, but tangential velocity is directly proportional to both. If you quadruple the radius, you must halve the rotation rate, which still gives you double the linear velocity. Larger stations require lower rotation rates, but higher tangential velocities. (As the radius of curvature increases, the speed along that curve must increase to maintain the same acceleration.) And in this case, it seems to be that tangential velocity that's of interest, not the rotation rate.

Ah right. That's why it threw me. One goes up, the other down.

Large stations are preferred because, ideally, you want the rotation rate as low as possible (less disorientation, less Coriolis Effects, etc) but you do end up with a higher tangential velocity (though the everyday occupants don't concern themselves much about that.)

 

[brainstorm]

The force is proportional to the radius and to the square of angular velocity, but tangential velocity is directly proportional to both. If you quadruple the radius, you must halve the rotation rate, which still gives you double the linear velocity. Larger stations require lower rotation rates, but higher tangential velocities. (As the radius of curvature increases, the speed along that curve must increase to maintain the same acceleration.) And in this case, it seems to be that tangential velocity that's of interest, not the rotation rate.

Does this mean that a very large space station could rotate very slowly to generate 1G of AG? Would that mean that weightlessness would be achieved with relatively little antispinward acceleration? That seems counterintuitive somehow, but only because I can't imagine my weight increasing or decreasing drastically due to small variations in speed.

 

[DaveC426913]

Does this mean that a very large space station could rotate very slowly to generate 1G of AG?

No. It would complete one revolution in a long time, but its actual tangential velocity would be quite high.

(Being in a rotating space station is kind of like climbing a slope curving upward but never reaching the top. A big space station is like climbing a long, gentle slope very fast, whereas a small SS is like climbing a short steep slope much slower. Not sure if that helps.).

See, the bigger the station, the more it emulates a real planet. That's why we would prefer one. It also means all the cool effects go away. You end up having to have normal airplanes instead of gossamer wings.

 

[brainstorm]

No. It would complete one revolution in a long time, but its actual tangential velocity would be quite high.

(Being in a rotating space station is kind of like climbing a slope curving upward but never reaching the top. A big space station is like climbing a long, gentle slope very fast, whereas a small SS is like climbing a short steep slope much slower. Not sure if that helps.).

See, the bigger the station, the more it emulates a real planet. That's why we would prefer one. It also means all the cool effects go away. You end up having to have normal airplanes instead of gossamer wings.

Ok, according the following calculator a space station of radius 10m rotating at 22mph would generate almost 1G of AG.

http://www.calctool.org/CALC/phys/Newtonian/centrifugal

At 11mph the AG seems to go down to @0.25G. So how would you maintain traction as you accelerate all the way to 22mph? It seems like you would be moon-jumping by the time you reached 11mph.

 

[DaveC426913]

Ok, according the following calculator a space station of radius 10m rotating at 22mph would generate almost 1G of AG.

Yikes. That's one revolution every 6 seconds.

At 11mph the AG seems to go down to @0.25G. So how would you maintain traction as you accelerate all the way to 22mph? It seems like you would be moon-jumping by the time you reached 11mph.

Yep. Probably. The trick of course, would be to use a mode of transport that is more efficient at forward movement with not as much pumping up and down energy wasted like with human legs. A bicycle would get you much closer, but you'd still reach a point of diminishing returns. And you'd always have a little air drag, so it would be a losing battle to get all the way up to 22. Before you ever get to zero, your wings would take over.


BTW, note that in a smaller SS this is needlessly complex way to accomplish your goal. If you simply leap up, you can reach the centre of the SS. Tangential velocity there approaches zero, so you're pretty much automatically weightless. No need to bother getting up any speed - that's for rim-huggers down there, not axis-flyers...

 

[mugaliens]

Large stations are preferred because, ideally, you want the rotation rate as low as possible (less disorientation, less Coriolis Effects, etc) but you do end up with a higher tangential velocity (though the everyday occupants don't concern themselves much about that.)

As it turns out, the stress of a smaller, 3 rpm toroid maintaining 1 g is far less than that on a larger 1 rpm toroid maintaining the same 1 g. Less stress means less weight, less cost, and faster construction time for any given interior volume. 3 rpm isn't ideal. It's just the fastest you can rotate it without causing too many issues with the humans inside due to coriolis, although some will become casualties. A 2 rpm toroid might be a decent compromise.

Toroids are preferred for a variety of reasons. The long cylinders envisioned by Gerard K. O'Neil aren't practical due to stablity reasons, and the greater the interior radius, the greater the stress on the pressure containment vessle. Toroids are also much easier to segment into separate pressure and fire containment areas. Without active stabilization, a cylinder will tumble, and the result would be catestrophiic. Multiple rotating toroids, on the other hand, can be linked to central non-rotating passageway at the axis. Care still needs to be taken, however, to disconnect precession forces between hubs, or you'll quickly wind up with an effective and unstable cylinder anyway.

 

[brainstorm]

Yikes. That's one revolution every 6 seconds.

But if the station didn't have windows, how would you even notice it was rotating except b/c of the AG?

A bicycle would get you much closer, but you'd still reach a point of diminishing returns. And you'd always have a little air drag, so it would be a losing battle to get all the way up to 22. Before you ever get to zero, your wings would take over.

But what happens first, the wings gaining lift or the bicycle tire slipping from lack of weight to create traction?

BTW, note that in a smaller SS this is needlessly complex way to accomplish your goal. If you simply leap up, you can reach the centre of the SS. Tangential velocity there approaches zero, so you're pretty much automatically weightless. No need to bother getting up any speed - that's for rim-huggers down there, not axis-flyers...

The calculator says that even with only 3m radius it takes 12mph to achieve 1G. 6m is not must of a flight, although I wouldn't want to try it off a roof. Sounds more like a difficult circus stunt than flying.

 

[DaveC426913]

As it turns out, the stress of a smaller, 3 rpm toroid maintaining 1 g is far less than that on a larger 1 rpm toroid maintaining the same 1 g. Less stress means less weight, less cost, and faster construction time for any given interior volume.

Well of course. This is always the case - more ambitious structures are more challenging and more demanding. If this weren't the case - if larger structures were not subject to more stresses etc., then we'd start low-tech by building large structures (like skyscrapers) and, as our technology improved our structures would get smaller (like bungalows) ... ne-eyebrow-cocked:

Instead, as is always the case, engineering effort is traded off in favour of end-usage of the structure (which is almost always larger=better).

 

[brainstorm]

Well of course. This is always the case - more ambitious structures are more challenging and more demanding. If this weren't the case - if larger structures were not subject to more stresses etc., then we'd start low-tech by building large structures (like skyscrapers) and, as our technology improved our structures would get smaller (like bungalows) ... ne-eyebrow-cocked:

Instead, as is always the case, engineering effort is traded off in favour of end-usage of the structure (which is almost always larger=better).

What if you factor in cost per unit area as well as long term maintenance costs? It might be that lots of simple and easy to maintain bungalows are more cost effective than big buildings. Plus, haven't you ever heard that the most urban growth in the 21st century will not occur in towering metal and glass but in user-fabricated shanty slums constructed of recycled building materials and scraps?

 

[DaveC426913]

But if the station didn't have windows, how would you even notice it was rotating except b/c of the AG?

The Coriolis Effects would be quite pronounced. You would feel yourself going in a circle.

But what happens first, the wings gaining lift or the bicycle tire slipping from lack of weight to create traction?

Well, lift of course will begin the moment you are moving, and ramp up from there, whereas traction will stay constant to a point then begin dropping rapidly to zero. So...

 

[dbell5]

Why are the speeds actually even different? Isn't the G-force just a product of the momentum of the objects inside the station. So shouldn't any object move with 1G of force if it is accelerating at a given rate?

The *aapparent* artificial gravitational force has nothing to do with momentum of the objects inside thje station. It is actually centripetal force (what most people call centrifugal force) caused by the station's wall pushing up against your feet. If your motion was in a straight line (a tangent to the station's curve), there would be no upward force. But any given point on the station's wall is constantly being accelerated away from that straight line, toward the center, into a closed, circular curve. It is that acceleration that results in the force you would feel.

Dave

 

[cjameshuff]

Toroids are preferred for a variety of reasons. The long cylinders envisioned by Gerard K. O'Neil aren't practical due to stablity reasons, and the greater the interior radius, the greater the stress on the pressure containment vessle. Toroids are also much easier to segment into separate pressure and fire containment areas. Without active stabilization, a cylinder will tumble, and the result would be catestrophiic. Multiple rotating toroids, on the other hand, can be linked to central non-rotating passageway at the axis. Care still needs to be taken, however, to disconnect precession forces between hubs, or you'll quickly wind up with an effective and unstable cylinder anyway.

Cylinders that aren't too spindly could be stabilized with tethers/booms at the periphery, and pairs of cylinders could be used. The instability's not a big enough issue to avoid the use of cylinders if they're otherwise more convenient.

Alternatively, you could have a high mass, slowly counterrotating outer shell...that provides a low gravity environment that would be useful for heavy machinery, takes mass off the high gravity inner section, allows for more shielding and machinery mass without adding to the structural mass required, provides a slow rotating outer shell that would be easier for spacecraft to rendezvous with, and let's you zero out the net angular momentum of the structure, eliminating the instability you mention.

For smaller structures, a habitat section and a counterweight linked by tethers allow a large radius of rotation without requiring a large monolithic structure.

 

[dbell5]

Funny that these same calculations result in a counter-proof to the hollow-Earthers (Koreshian cosmogony):
If we did inhabit the inside surface of a hollow sphere the size of the Earth, the centripetal acceleration at the equator would be over 3G...

 

[brainstorm]

Funny that these same calculations result in a counter-proof to the hollow-Earthers (Koreshian cosmogony):
If we did inhabit the inside surface of a hollow sphere the size of the Earth, the centripetal acceleration at the equator would be over 3G...

So there is more force than just gravity holding the planet together?

 

[DaveC426913]

Funny that these same calculations result in a counter-proof to the hollow-Earthers (Koreshian cosmogony):
If we did inhabit the inside surface of a hollow sphere the size of the Earth, the centripetal acceleration at the equator would be over 3G...

How do you figure 3Gs?

If that were true, it would apply to the outer surface as much as the inner surface. What you are suggesting is that, standing on the outer surface of the Earth, I am experiencing a 3G pull away from the Earth!

 

[dbell5]

How do you figure 3Gs?

If that were true, it would apply to the outer surface as much as the inner surface. What you are suggesting is that, standing on the outer surface of the Earth, I am experiencing a 3G pull away from the Earth!

Huh! That would appear to be so! (Actually, 2G away, since the Earth's field is 1G inwards at the surface, vs. 0G inside a hollow shell.)

OK, here's how I got there:
a = v^2/r
Circumference of Earth is about 41,000 km, or 41e6 meters
Rotation is once in 86,400 seconds, for a tangential velocity of about 474 m/s.
Radius is about 6,500 km, which is where I went wrong - I divided by 6,500, not 6.5e6.
I got 34 m/s^2, should be 0.034 m/s^2

OK, so we're in no immediate danger of flying off into space!

Dave

 

[dbell5]

A corollary to the above that I never thought of is that, even if the Earth were a perfect, homogeneous sphere, and ignoring the bulky clothes, I'd weigh nearly 5 pounds more at the poles than I do here at 37°N!