Getting the Science Right, Part 2

[Brown]

Several years ago, I toyed around with writing a story about a space station. The space station was a wheel-type station very similar to the space station depicted in "2001: A Space Odyssey" except that it had more levels or "floors," if you will.

Basically, the premise of the story was that the space station was a kind of resort. The station included research facilities, but a large portion of one "wheel" was set aside for recreational activities.

The space station was large, a kilometer in diameter. Accordingly, the outermost ("lowest") level was five hundred meters from the center of rotation. The perceived "gravity" at this point was one g, or about 9.8 meters per second squared.

In development of the idea, I considered the following questions. I pose them here for entertainment value.

Question 1: How fast did the space station need to rotate to create this perceived gravity, in units of seconds per rotation? (Related: was the space station in "2001" rotating at an appropriate rate? Also: How fast would the space station need to rotate if it were two kilometers in diameter instead of one kilometer in diameter?)

Question 2: One of the "higher" levels, closer to the center of rotation, was the "lunar level," at which the perceived gravity was about one-sixth g, or 1.6 meters per second squared. The purpose of such a level would be to acclimate lunar travelers to the gravity of the Moon. How far is the "lunar level" from the center of rotation?

Question 3: One of the lower levels of the space station (gravity close to one g) has a swimming pool. Sloshing water from pool is to be avoided. Should there be any modifications to the pool in order to prevent this hazard? What will the water in the pool look like? (E.g., will the surface be flat? Will water "pile up" on one side of the pool?)

Question 4: One of the lower levels of the space station has a miniature golf course. Under what conditions, if any, will a putt roll "true?"

Question 5: If a golfer holds a golf ball one meter directly over his right toe and drops it, will the ball "fall" straight down and land on his right toe? (The notion of how objects "fall" could have consequences for things such as diving into the pool, taking a shower, or going to the bathroom.)

Question 6: People on the Earth cannot "feel" the Earth rotating. Could people on the space station "feel" the station rotating?

And finally: What other considerations would need to be taken into account by a developer that wanted to create a space-based resort?

I found that posing questions like this, and trying to answer them with scientific accuracy, could help create a more vivid description of the environment.

[Johnny Pneumatic]

#3 The pool's surface will curve like the pool's "bottom"; but with a steeper slope to it I think.

[tracer]

Originally posted by Brown
One of the "higher" levels, closer to the center of rotation, was the "lunar level," at which the perceived gravity was about one-sixth g, or 1.6 meters per second squared.
Babylon 5 also featured a space station that rotated to produce artificial gravity. On the Babylon 5 station, the outermost levels (where the gravity was the strongest) were called "downbelow", and were the place where all the misfits and scumbags were relegated to. Apparently, the Low Gravity district was also the High Rent district.

[chance]

Question 3: One of the lower levels of the space station (gravity close to one g) has a swimming pool. Sloshing water from pool is to be avoided. Should there be any modifications to the pool in order to prevent this hazard? What will the water in the pool look like? (E.g., will the surface be flat? Will water "pile up" on one side of the pool?) Curved surface. Don’t have the diving board too close to the edge! See lower for reason.

Question 4: One of the lower levels of the space station has a miniature golf course. Under what conditions, if any, will a putt roll "true?" I don’t see a problem here (assuming putting). Driving from a green however may introduce problems.

Question 5: If a golfer holds a golf ball one meter directly over his right toe and drops it, will the ball "fall" straight down and land on his right toe? (The notion of how objects "fall" could have consequences for things such as diving into the pool, taking a shower, or going to the bathroom.) Yes, any object that changes it’s ‘hight’ will follow a curved path (conservation of momentum) modified by the atmospheric drag.

Question 6: People on the Earth cannot "feel" the Earth rotating. Could people on the space station "feel" the station rotating? No, only if there is a change.

And finally: What other considerations would need to be taken into account by a developer that wanted to create a space-based resort? how to correctly align the toilet paper on the roll, I can’t believe they still get this wrong, I mean how simple is this, it’s not like you need to be a rocket scientist or anything.

[Matabiri]

Question 1: How fast did the space station need to rotate to create this perceived gravity, in units of seconds per rotation?

I get 44.9 seconds/rotation, although I may have dropped a factor of a half somewhere...

(Related: was the space station in "2001" rotating at an appropriate rate? Also: How fast would the space station need to rotate if it were two kilometers in diameter instead of one kilometer in diameter?)

63 s/rev

Question 2: One of the "higher" levels, closer to the center of rotation, was the "lunar level," at which the perceived gravity was about one-sixth g, or 1.6 meters per second squared. The purpose of such a level would be to acclimate lunar travelers to the gravity of the Moon. How far is the "lunar level" from the center of rotation?

83 m, I think.

[Brown]

Originally posted by Matabiri
Question 1: How fast did the space station need to rotate to create this perceived gravity, in units of seconds per rotation?

I get 44.9 seconds/rotation, although I may have dropped a factor of a half somewhere...This is correct. I found the answer surprising because it means that you have to rotate a pretty large space station rather fast to get one g. (Arthur C. Clarke has suggested that space stations would rotate more slowly, to give the sensation of less than one g.)

The computation goes like this: for uniform rotation (i.e., the wheel rotating at a constant radial velocity), radial acceleration (in meters per second per second) equals radius (in meters) times radial velocity (in radians per second) squared. The radial acceleration is given as 9.8 meters per second per second, and the radius is given as 500 meters. Radial velocity is easily computed as 0.14 radians per second. There are 2*pi radians in a revolution, so 0.14 radians per second = 0.14/(2*pi) = 0.0223 revolutions per second. Take the inverse, and you get about 44.9 seconds per revolution.

If the radius is 1000 meters, then you can spin the station slower to get one g, but the station still has to spin pretty fast. Again, Matabiri's answer is correct.

To find the "lunar level," use the same radial velocity (0.14 radians per second) and let radial acceleration be 1.6 meters per second squared, and solve for the radius. The lunar level is at about 82 meters from the center.

As for objects "falling" on a space station, consider that according to Newtonian mechanics, an object tends to go in a straight line unless acted upon by a force. Would a dropped object on a space station be acted upon by a force? Would the object fall in a straight line directly away from the center of the space station? Would the fact that the station is rotating cause a straight path to appear curved?

[SGT]

Originally posted by Brown

As for objects "falling" on a space station, consider that according to Newtonian mechanics, an object tends to go in a straight line unless acted upon by a force. Would a dropped object on a space station be acted upon by a force? Would the object fall in a straight line directly away from the center of the space station? Would the fact that the station is rotating cause a straight path to appear curved?

For an observer in an inertial frame, outside the station, the object would follow a straight line with the tangential velocity it initially had. Since the station floor is curved, the object will eventually hit the floor.
Since the station is rotating, the object will hit the floor behind the 'vertical' it initially belonged to.
An observer rotating with the station will see a curved path.

BTW, I obtained the same results as Matabiri and you. And I was surprised too.

[DickK]

Originally posted by Brown
...As for objects "falling" on a space station, consider that according to Newtonian mechanics, an object tends to go in a straight line unless acted upon by a force. Would a dropped object on a space station be acted upon by a force? Would the object fall in a straight line directly away from the center of the space station? Would the fact that the station is rotating cause a straight path to appear curved? Assuming the object is not at the the centre of the hub, and in the absence of any mathematical skill, is it that the apparent fall of any object would be straight down, along a line intersecting the station hub and the original position of the dropped object? I suspect it may curve, with respect to the orientation of the start of the drop, but that the increasing acceleration of gravity as it proceeds to the rim combined with any lateral acceleration component from the spin of the station at drop time results in the effect. Not sure what might happen if it were dropped from the station's centre of mass, a back hand lob? Thinking about it, you couldn't drop it from that position, could you?

[wollery]

I think that if you drop a object it will appear to fall straight down, when what it is actually doing is travelling at a tangent to the point at which it was released.

Remember that when you let it go it has a momentum in the direction that the space station is rotating. There is now no force acting on it, so it will simply continue in a straight line, but the floor of the space station is in it's path. I haven't done the maths, but I'm pretty sure that the time it takes for the object to reach the intersection point of floor that's in it's path is the same as the time it takes for the point that was directly below it to rotate to that same intersection point.

I think that makes sense! :confused:

[SGT]

Originally posted by wollery
I think that if you drop a object it will appear to fall straight down, when what it is actually doing is travelling at a tangent to the point at which it was released.

Remember that when you let it go it has a momentum in the direction that the space station is rotating. There is now no force acting on it, so it will simply continue in a straight line, but the floor of the space station is in it's path. I haven't done the maths, but I'm pretty sure that the time it takes for the object to reach the intersection point of floor that's in it's path is the same as the time it takes for the point that was directly below it to rotate to that same intersection point.

I think that makes sense! :confused:

Nope! The tangential velocity of the body is less then the tangential velocity of the floor. The body will describe a straight line equal to V₁t. In the same time, the position where it originally was, will describe an arc with the same length. The angle the original position describes is &omega;t, while the angle described by the body is tan^-1(R₁/V₁t) < &omega;t, where &omega; is the angular velocity and R₁ is the distance from the original position to the center of the station. So the body will fall behind the apparent vertical and the observer inside the station will see a curved path.

[Benguin]

Originally posted by Brown

And finally: What other considerations would need to be taken into account by a developer that wanted to create a space-based resort?

Care would have to be taken with the atmospherics .... presence of any heavier than air gas would tend to the outer ring and suffocate people out there, whilst lighter-than-air ones would get the residents nearer the hub.

In order to get adequate air exchange for for comfort, health and climate control a massive HVAC system would need to be in place, either that or some sort of nifty micro-metereology system. Little clouds and mini thunderstorms!

Probably also need some contingency in place for the utter chaos caused by a change in angular velocity!

[wollery]

Originally posted by SGT
Nope! The tangential velocity of the body is less then the tangential velocity of the floor. The body will describe a straight line equal to V₁t. In the same time, the position where it originally was, will describe an arc with the same length. The angle the original position describes is &omega;t, while the angle described by the body is tan^-1(R₁/V₁t) < &omega;t, where &omega; is the angular velocity and R₁ is the distance from the original position to the center of the station. So the body will fall behind the apparent vertical and the observer inside the station will see a curved path. Yeah, I did the maths last night. It was fairly obvious as soon as I drew a little cartoon sketch that I was wrong. :(

Oh well, there you go. ;)

[SGT]

Originally posted by SGT
Nope! The tangential velocity of the body is less then the tangential velocity of the floor. The body will describe a straight line equal to V₁t. In the same time, the position where it originally was, will describe an arc with the same length. The angle the original position describes is &omega;t, while the angle described by the body is tan^-1(R₁/V₁t) < &omega;t, where &omega; is the angular velocity and R₁ is the distance from the original position to the center of the station. So the body will fall behind the apparent vertical and the observer inside the station will see a curved path.

Actually the angle described by the body is tan^-1(V₁t/R₁) < &omega;t. I inverted the sides of the triangle, but the reasonig is still valid, as wollery checked.

[Ziggurat]

Originally posted by Benguin
Care would have to be taken with the atmospherics .... presence of any heavier than air gas would tend to the outer ring and suffocate people out there, whilst lighter-than-air ones would get the residents nearer the hub.


That's actually not such a big problem, the thermal energy of the air will keep it fairly well mixed. Keep in mind that carbon dioxide is about 50% heavier than air, and it mixes pretty well down here on earth.

But what's a MAJOR issue is keeping the whole thing sealed up. The bigger your space station, the more possible places for leaks to occur. And if they occur too often, you'll spend too much time/money/energy/whatever chasing them down and hauling air up to replace what you lose. This isn't necessarily an insurmountable obstacle, but it is a big one that you'd need to spend a LOT of design and constructon effort to minimize.

[Benguin]

Originally posted by Ziggurat
That's actually not such a big problem, the thermal energy of the air will keep it fairly well mixed. Keep in mind that carbon dioxide is about 50% heavier than air, and it mixes pretty well down here on earth.


Very true, but we do have lot's of air movement through meterological effects and more localised convection etc to keep it all mixing up. I'm sure 'brownian motion' (OK, I know, I can't remember the proper physics term!) alone isn't enough to keep us all from gasping.

If you think, it isn't far above our surface that we have some fairly active turbulence stirring the atmosphere up, kept going by vast amounts of thermal energy from the sun. Our station could get pretty stagnant without care.

But what's a MAJOR issue is keeping the whole thing sealed up. The bigger your space station, the more possible places for leaks to occur. And if they occur too often, you'll spend too much time/money/energy/whatever chasing them down and hauling air up to replace what you lose. This isn't necessarily an insurmountable obstacle, but it is a big one that you'd need to spend a LOT of design and constructon effort to minimize.

There would be significant risks associated with breaches and, though micro-meteorite strikes would be a danger, I think the major risks comes from accidents inside. Explosions, fires, or even things falling under internal gravity present a very clear danger to the membrane.

[wollery]

Okay, so this is really sad, and I'm not sure I should admit to this, but......

After doing the maths to see if a dropped object followed a curved path I was wondering just how far behind the original drop point it would fall, and how it would vary with the height it was dropped from.

So I wrote a computer program to calculate it!

I know, I'm a sad geek, but the results are quite interesting, assuming a radius of 500m;
drop height; 1m, distance; 4.225 cm
drop height; 2m, distance; 11.98 cm
drop height; 10m, distance; 1.361 m
drop height; 50m, distance; 16.65 m
drop height; 100m, distance; 53.25 m
drop height; 200m, distance; 203.02 m
drop height; 300m, distance; 566.00 m
drop height; 400m, distance; 1.764 km
drop height; 490m, distance; 24.22 km (which is almost 8 times round the station!)

Well I thought it was interesting!
And besides, it distracted me from real work for 20 minutes.

[alfaniner]

One thing I've always considered about this -- The higher up you drop from, the less "sideways" velocity it will have. So, dropping from the center, (or throwing, as the center would have no perceived gravity at all), the "bottom" of the space station would continue rotating past, while the object continues in a straight line with respect to its origin.

If there is a building or a large wall at the "bottom", this will be moving at 44.9 second's rotation. Therefore, while the landing might be soft (at only the speed the object was dropped/thrown, it will very probably be smashed from the side as the rotating objects encounter it.

Imagine hanging slightly above the center of one of those carnival cyclotron spinning rides. Now throw a ball at one of the riders. You will hit the side of the little cubicle of a rider farther along the circle.

However, if you are off center, and attached to (rotating with) the ride, I can see where the mental puzzle gets a little more difficult.

[Brown]

It's been explained above that a dropped body will not fall along an apparently vertical path, and the observer inside the station will see the object follow a curved path. This is correct, and I was mildly surprised by this, too.

Some folks think that if you let an object go, "zero gravity takes over" and the object just floats in the air. Actually, as has been described, the object follows a straight line tangent path, which is interrupted by the floor of the station.

Some other folks also think that if you let the object go, it follows a path directly away from the center of the wheel, being pushed in that direction by "centrifugal force."

In light of the effect on falling objects, someone might want to tackle the question of whether it would be possible to "feel" the station rotating. (If they can "feel" it rotating, there is a possibility that guests will experience motion sickness.)

My computations pertaining to falling objects caused me to wonder whether it would be feasible to put a miniature golf course on a space station. Should the putting greens be flat, or curved to match the curvature of the station? Does it matter the ball is hit in the direction of rotation or perpendicular to the direction of rotation? When putted, will the ball roll "true?"

If memory serves, a miniature golf hole could be designed so that a putt rolls "true." But a hole could also be designed so that a putt would roll in odd ways, even though the putting surface looks flat. This could make for an interesting miniature golf course. You wouldn't need no stinkin' windmills to make it challenging.

Atmospheric circulation and airlock considerations have been mentioned. Here are a few other considerations that might be taken into account by a developer that wanted to create a space-based resort: mechanized transportation from one site on the station to another, without adversely affecting the spin of the station (darn that conservation of angular momentum!); evacuation plans in the event of a radiation hazard; a heavily shielded section to serve as a "lifeboat" in the event not everyone can be evacuated; development of a zero-g recreational room (you know people would want to do that!) and activities that would be permitted therein; and techniques and apparatus (such as bars, ropes, padding, etc.) for moving people safely from a zero-g environment in their spaceships docked in the hub to the outer levels of the station.

Edited to add a "dropped" word.

[Brown]

Originally posted by alfaniner
One thing I've always considered about this -- The higher up you drop from, the less "sideways" velocity it will have. So, dropping from the center, (or throwing, as the center would have no perceived gravity at all), the "bottom" of the space station would continue rotating past, while the object continues in a straight line with respect to its origin.

If there is a building or a large wall at the "bottom", this will be moving at 44.9 second's rotation. Therefore, while the landing might be soft (at only the speed the object was dropped/thrown, it will very probably be smashed from the side as the rotating objects encounter it. Great point. I considered this in connection with having a "high dive" feature above the resort pool. Basically, the diver would jump from a considerable height (and would jump in such a way that he would indeed go into the pool) and would fall fairly slowly toward the water.

Sounds like fun. But the water is eventually going to hit him harder than he thinks, and from a direction that may catch him off guard.

[wollery]

Originally posted by Brown
In light of the effect on falling objects, someone might want to tackle the question of whether it would be possible to "feel" the station rotating. (If they can "feel" it rotating, there is a possibility that guests will experience motion sickness.) Ignoring everything else in that post (although the golf idea is intriguing) motion sickness derives from changes in the direction and rate of motion, ie non-constant acceleratoins and velocities. In this space station there is only one acceleration, which I hope would be smooth, and this is directed radially inwards. I see no reason why anyone should feel motion sickness.

Unless of course they look out the side window and see the Earth and stars rotating at 0.14 rad/s! ;)

[wollery]

Originally posted by Brown
Great point. I considered this in connection with having a "high dive" feature above the resort pool. Basically, the diver would jump from a considerable height (and would jump in such a way that he would indeed go into the pool) and would fall fairly slowly toward the water.

Sounds like fun. But the water is eventually going to hit him harder than he thinks, and from a direction that may catch him off guard. Also you'd want to make sure that your 10 metre high board was way out over the pool, or the diver may not even make it to the water!

[Brown]

One more thing. We are used to having dropped objects fall slowly and speeding up as they fall. As we all know, the speed of an object increases by about 9.8 m/s (32 ft/s) for every second it is in free-fall. Would anyone care to describe the apprarent acceleration of a dropped object on the station? Would it appear to fall slowly at first and speed up as it hit the floor?

[Brown]

Originally posted by wollery
Also you'd want to make sure that your 10 metre high board was way out over the pool, or the diver may not even make it to the water! Exactly. I was thinking that the diver might start even higher up than that, so that he could do lots of flips and twists if he wished to do so. The problem is that the diver could not "aim for the pool." There would have to be some sort of aiming target (and some sort of safety feature in the event the target was missed). Or the diver would not be allowed to aim his jump at all. Instead, he would only be given the option of doing a dead drop, rather than a "dive."

[Brown]

Originally posted by wollery
Ignoring everything else in that post (although the golf idea is intriguing) motion sickness derives from changes in the direction and rate of motion, ie non-constant acceleratoins and velocities. In this space station there is only one acceleration, which I hope would be smooth, and this is directed radially inwards. I see no reason why anyone should feel motion sickness.Ah, the space station might be constant, but the patrons might change their orientation. Might they perceive a different "gravity" by doing an about face or turning their heads?

If the patrons always looked in a single direction, then they would probably have little or no difficulty.

[SGT]

Originally posted by Brown

My computations pertaining to falling objects caused me to wonder whether it would be feasible to put a miniature golf course on a space station. Should the putting greens be flat, or curved to match the curvature of the station? Does it matter the ball is hit in the direction of rotation or perpendicular to the direction of rotation? When putted, will the ball roll "true?"



Edited to add a "dropped" word.

The curving path is due to Coriolis acceleration, wich rises in a rotating system when an object changes its distance to the rotation axis.
In a flat putting green the ball would change its distance to the rotation axis and would be deflected. In a curved green, matching the curvature of the station the ball would follow a straight path.

[Matabiri]

Originally posted by Brown
One more thing. We are used to having dropped objects fall slowly and speeding up as they fall. As we all know, the speed of an object increases by about 9.8 m/s (32 ft/s) for every second it is in free-fall. Would anyone care to describe the apprarent acceleration of a dropped object on the station? Would it appear to fall slowly at first and speed up as it hit the floor?

There's no force acting on it, so it won't accelerate at all. There'll be a perceived horizontal (i.e. parallel to the floor) acceleration, though, as described above.

[SGT]

Originally posted by Matabiri
There's no force acting on it, so it won't accelerate at all. There'll be a perceived horizontal (i.e. parallel to the floor) acceleration, though, as described above.

For an observer in the rotating frame the falling object will be subjected to an acceleration equal to 2&omega;V, where &omega; is the angular velocity of the rotating frame and V is the linear velocity of the object.

[wollery]

Originally posted by Matabiri
There's no force acting on it, so it won't accelerate at all. There'll be a perceived horizontal (i.e. parallel to the floor) acceleration, though, as described above. There's also a perceived vertical acceleration. You only have to draw a simple vector diagram to see that when dropped its velocity has no vertical component (relative to the floor), but does by the time it hits the floor.

[Brown]

Personally, I find thought experiments like this to be very enjoyable and very valuable. It would be one thing for me to write my story about a space-based resort by saying, "It will be just like Earth, except the floor will be curved." (In "2001," the space station and the Discovery centrifuge were basically handled in this fashion.)

Except it won't be like Earth. The "artificial" gravity behaves differently from the gravity we're used to. If you stand still, you might not be able to notice much difference. But if you walk, will you have to adjust your gait to avoid the sensation of falling over? If you sit down, will you get a sensation that you might miss your chair? When you dress, will you need to steady yourself when putting on your pants? If you use the toilet, will there a have to follow special procedures or use equipment with special modifications?

A person arriving at such a space-based resort might see some pretty weird things, or might be exposed to some pretty weird procedures or effects. Patrons might be required, for example, to take a "safety test" or might be obligated to learn the meaning of different alert annunciators. They might have to take medication to deal with the disorientation. (Some folks operating in micro-gravity take scopalomine, I understand.) Sports such as tennis might be so difficult that it might not make sense to offer them.

Part of the enjoyment associated with dreaming up this fantasy station is trying to figure out what weird stuff will patrons encounter, and is there a reason for it?

[Matabiri]

Originally posted by wollery
There's also a perceived vertical acceleration. You only have to draw a simple vector diagram to see that when dropped its velocity has no vertical component (relative to the floor), but does by the time it hits the floor.

Ah yes; I see where I went wrong.

[Brown]

Originally posted by bewareofdogmas
#3 The pool's surface will curve like the pool's "bottom"; but with a steeper slope to it I think. The surface of the pool was one subject for which I was never able to be satisfied with my answer. At one point, I thought that the surface of the water would be curved, but that the water would also be piled a little higher on the trailing side than on the leading side. But I am not sure about this. Hydraulics is not my field.

[wollery]

Originally posted by Brown
The surface of the pool was one subject for which I was never able to be satisfied with my answer. At one point, I thought that the surface of the water would be curved, but that the water would also be piled a little higher on the trailing side than on the leading side. But I am not sure about this. Hydraulics is not my field. Again, there's no tangential acceleration, so I see no reason why the water should be deeper at one end than the other. I think that the surface would be spherically curved, thus the depth will be constant, assuming that the bottom of the pool is a spherical arc of the space station. Forget that the space statipon is rotating for a moment a try thinking of it as a static situation where gravity acts radially outwards from the centre.

[Matabiri]

Originally posted by wollery
Again, there's no tangential acceleration, so I see no reason why the water should be deeper at one end than the other. I think that the surface would be spherically curved, thus the depth will be constant, assuming that the bottom of the pool is a spherical arc of the space station. Forget that the space statipon is rotating for a moment a try thinking of it as a static situation where gravity acts radially outwards from the centre.

There would be a problem with any splashed water, though. As it rose into the air it would appear to accelerate in the direction of rotation, and might well splash the wall in front of you.

Edit it to add: by about 14cm per second/m "elevation", so not by much.

[wollery]

Okay, this one is hurting my head, and I'm going to the pub for a beer as soon as I've posted this.

What happens to an object if you throw it up into the air, ie directly at the hub?

I know that it will depend on how hard you throw it, but by analogy with the falling object would it not appear to leap forward as it's thrown up and then follow a curved path going out ahead of and "up" from the spot it was thrown from until it reaches a "highest point" and then it will act as though it was dropped from that point.

I just can't seem to get my head around what the path of the flight will look like from the reference frame of the space station. :(

I need a drink!

[Brown]

Originally posted by wollery
Again, there's no tangential acceleration, so I see no reason why the water should be deeper at one end than the other. I think that the surface would be spherically curved, thus the depth will be constant, assuming that the bottom of the pool is a spherical arc of the space station. Forget that the space statipon is rotating for a moment a try thinking of it as a static situation where gravity acts radially outwards from the centre. You may be right. As I said, I was never quite satisfied with whether the "falling" anomaly would have any effect on a body of water.

As has been mentioned, the radial acceleration vector points inward, toward the hub, in the "up" rather than the "down" direction. What patrons perceive as gravity is really the force of the station pushing their feet to keep them from going in a straight line, and the reactive force applied to the station by their feet. As you imply, in statics, the forces balance. If the forces don't balance, the item moves and is not static. A person standing still on the station has a force applied by the station against his feet toward the direction of the hub. To keep things in balance from the patron's viewpoint, the feet apply an equal and opposite force against the station, in the direction away from the hub. It is this reactive force applied by the feet that some people call "centrifugal force," which seems to be directed away from the center of the hub. If the floor were to suddenly disappear, however, the person would not move in the direction of the "centrifugal force" but would actually move in a perpendicular direction. Hard to describe.

[SGT]

Originally posted by wollery
Okay, this one is hurting my head, and I'm going to the pub for a beer as soon as I've posted this.

What happens to an object if you throw it up into the air, ie directly at the hub?

I know that it will depend on how hard you throw it, but by analogy with the falling object would it not appear to leap forward as it's thrown up and then follow a curved path going out ahead of and "up" from the spot it was thrown from until it reaches a "highest point" and then it will act as though it was dropped from that point.

I just can't seem to get my head around what the path of the flight will look like from the reference frame of the space station. :(

I need a drink!

There is no real gravity in the station, so an object thrown in the air will not decelerate unless due to air resistance.
Neglecting air resistance, the object will simply keep it's verticl velocity.
If the station was not rotating, the object would simply hit the rim in a position diametrally opposed to the throwing point. Since the station is rotating, the object has an horizontal velocity too, so it will move according to the composition of both velocities. For instance, if the vertical component is equal to the horizontal one, the object will hit the rim at 90^o of the throwing point. In the same time, the station will rotate by an angle of 1 radian (~57.3^o), so the object will 'fall' in a position ahead of the initial one.

nitpick
The water of the pool will have a cilindrical and not spherical surface, but the physics you used is correct.

[Brown]

Originally posted by wollery
Unless of course they look out the side window and see the Earth and stars rotating at 0.14 rad/s! In the movie "2001," the space station had a lot of windows. When Floyd was in the station phone booth, the Earth was seen doing slow somersaults in the background.

I suspect that for a lot of people, this sight would be disorienting. Even watching the stars spin might cause vertigo. In addition, windows would be potential leak sites. Also, there would be times when the sun would shine through the windows and be blinding, so each window would probably have to be equipped with an automatic "shutter" of some type, adding to the expense.

I therefore envisioned a space station resort in which there were few windows. The general attitude of most science fiction shows, of course, is that space stations have LOTS of windows, each brilliantly lit from the station's interior lighting.

[Brown]

Originally posted by alfaniner
Imagine hanging slightly above the center of one of those carnival cyclotron spinning rides.... It's been a while since I was on one of these rides, but there is one thing that I remember distinctly. As the ride spun faster and faster, the shape of the spinning cylinder seemed to change. It looked more like a funnel than like a cylinder. This was an illusion, of course, as my brain tried to make sense of the notion that I was upright and unsupported, but not falling. My brain told me that I was leaning backwards, not that I was upright.

I wonder whether perceptions on a rotating space station would get skewed. Would one person standing a few meters from another person perceive that the other person was impossibly "leaning?" Would it appear that the other person is elevated?

It seems to me that the perception of elevation would be very likely. A person might find it somewhat uncomfortable to converse with another on the space station, because the person may find that he has to raise his chin more than he's used to, in order to look the other in the eye. The more distant the other, the more the chin must be raised. And the brain could interpret the raising of the chin (i.e., the general orientation of the head) as facing something that is at a higher elevation.

[Badly Shaved Monkey]

Originally posted by chance

No, only if there is a change.


(In response to whether people would "feel" the rotation.)

I don't think that's right, but would ask others to do the arithmetic.

I think I'm right in saying that the difference in angular velocity between head and foot would create a nauseating sensation as people moved especially if they bent down thereby moving their vestibular systems to a larger radius.

Basically for a realistically sized station the radius and rotational rate would mean these effects would be quite large. For an absolutely huge orbital with a vast radius and tiny rotation rate, the effects would become negligible.

I have read this somewhere as being an objection that makes rotating space stations pointless. Better just to put up with micro-g.

[Rolfe]

Some temptations are too great.... (http://www.midwinter.com/lurk/universe/setting-1.html)The Babylon Project was a dream given form. Its goal, to prevent another war by creating a place where humans and aliens could work out their differences peacefully. It's a port of call - home away from home for diplomats, hustlers, entrepreneurs, and wanderers. Humans and aliens wrapped in two million, five hundred thousand tons of spinning metal, all alone in the night. It can be a dangerous place, but it's our last best hope for peace. This is the story of the last of the Babylon stations. The year is 2258. The name of the place is Babylon 5....(Apologies if this has already been discussed, I haven't been following this thread.)

Rolfe.

[SGT]

Originally posted by Badly Shaved Monkey
(In response to whether people would "feel" the rotation.)

I don't think that's right, but would ask others to do the arithmetic.

I think I'm right in saying that the difference in angular velocity between head and foot would create a nauseating sensation as people moved especially if they bent down thereby moving their vestibular systems to a larger radius.

Basically for a realistically sized station the radius and rotational rate would mean these effects would be quite large. For an absolutely huge orbital with a vast radius and tiny rotation rate, the effects would become negligible.

I have read this somewhere as being an objection that makes rotating space stations pointless. Better just to put up with micro-g.

There is no difference in angular velocity between head and foot. There is a difference in linear velocity.

[Brown]

Originally posted by Badly Shaved Monkey
Basically for a realistically sized station the radius and rotational rate would mean these effects would be quite large. For an absolutely huge orbital with a vast radius and tiny rotation rate, the effects would become negligible.Just for kicks, how fast would "Ringworld" have to rotate to generate 1 g?

The radius would be, let's say, 150 million kilometers. If my math is right, one Ringworld "year" would be surprisingly short: about 9 days.

[Brown]

Originally posted by SGT
For an observer in the rotating frame the falling object will be subjected to an acceleration equal to 2&omega;V, where &omega; is the angular velocity of the rotating frame and V is the linear velocity of the object. I haven't verified the equation, but it seems a little high to me. The linear velocity would be V = &omega;r, and if the apparent acceleration is 2&omega;V, then the apparent acceleration would be 2&omega;²r. Since the radial acceleration is &omega;²r, the apparent falling acceleration would be twice the radial acceleration.

If the station were rotating to generate one g, the objects would appear to fall at 2g. This would mean that falling objects would appear to an observer to fall really fast.

Maybe the formula is correct, I don't know, or maybe my math is off.

[SGT]

Originally posted by Brown
I haven't verified the equation, but it seems a little high to me. The linear velocity would be V = &omega;r, and if the apparent acceleration is 2&omega;V, then the apparent acceleration would be 2&omega;²r. Since the radial acceleration is &omega;²r, the apparent falling acceleration would be twice the radial acceleration.

If the station were rotating to generate one g, the objects would appear to fall at 2g. This would mean that falling objects would appear to an observer to fall really fast.

Maybe the formula is correct, I don't know, or maybe my math is off.

I apologize for not being clear. I thought everybody was familiar with Coriolis' acceleration. The velocity in the formula is the radial component of velocity. Tangential velocity gives origin to no Coriolis acceleration, only to centripetal acceleration.
Both centripetal and Coriolis' accelerations are orthogonal to the velocity, so they don't change the modulus, only the direction.

[SGT]

Originally posted by Brown
Just for kicks, how fast would "Ringworld" have to rotate to generate 1 g?

The radius would be, let's say, 150 million kilometers. If my math is right, one Ringworld "year" would be surprisingly short: about 9 days.

I found 8.9924 days ~ 9 days, the same as you. The kinetic energy would be enormous.

[Badly Shaved Monkey]

Originally posted by wollery
For a station with a 1km diameter rotating to produce 1g, the difference in velocity between the feet and head of a person 1.8m tall is 27cm/s, less than 0.4% variation. I'm not sure if you could feel that, but I doubt it.

Ding!! Bell rings and lights go on in BSMs little simian brain.

I remember where I got my factoid from, now. It was a discussion of interplanetary/interstellar travel in which the idea of generating an acceleration to replace gravity was being discussed. It was talking about the idea of having a ship built with a rotating toroidal section for the crew to live in. So, the diameter would be much less than 1km (at least for ships we could envisage building in the near-term) and the effects would be much greater. The point being that passengers en route to Mars would have to deal with the consequences of long term micro-g and its consequent problems when arriving at either end of the journey.

Presumably there would need to be a calcuation of the costs and benefits of travelling in a small rapidly spinning ship. The discussion I saw implied it would be too horrid to experience to be desirable.

On the other hand, in the long future, or in a science fiction story, vast rotating ships slowly cruising around the Solar System or to other stars wold be feasible and once you get to these large sizes, you have created mini-worlds that, for the purposes of speculative stories, would be large enough to be contain significantly large and self-sustaining colonist populations.

[SGT]

Let's see if I can attach the picture with the path viewed by the rotating observer.

[SGT]

The picture I posted was obtained by using my equations, with the correction provided by Matabiri.
If we consider friction between the ball and the floor, during the shock, the floor will add a parcel of it's tangential velocity to the ball and the second part of the trajectory will probably be flatter.

[SGT]

Originally posted by rppa
Somewhere way back I remember reading that the Ringworld concept came about as a modification of Dyson spheres, which are entire closed spheres. People realized that these would be unstable, would begin drifting off center right away. I don't remember discussions of Ringworld instabilities, but I do seem to recall that Niven added thrusters to the story line at some point.

I didn't mention Ringworld in this discussion because it's just too darn big. It didn't seem relevant. Niven is spinning something which is the size of a planetary orbit. It maintains about 1 g, but needs much less angular velocity to do so, so the coriolis effects are a lot less noticeable on most scales.

It's been a long time since I read "Integral Trees" but my memory was that it dealt with dynamical issues on about a space-station scale. But somebody mentioned Clarke's "Rendezvous with Rama" and that is of course much more relevant. I think he goes into some detail on stuff like the behavior of water pools and what it's like to swim in them, and the weird way artificial weather acts inside the space station.

Any of these hard-science guys are well worth reading if you want to get the science right. They've given a lot of thought to how things work, and shown us how to work that stuff into an entertaining story line.

Brown has already made the calculations and obtained 9 days for Ringworld's year.
I think there would be a problem much more serious than instability with Ringworld: leakage of atmosphere. Since there is no real gravity in the world, any air molecule will move freely until finding another molecule or an obstacle and then it will bounce.
Since the direction of movement is random, several molecules will drift to Space to never be recovered again.
I think that Ringworlders would die from lack of oxigen much sooner than the instability effects could be sensed.

[SGT]

My mistake. Here is the real trajectory.

[Brown]

I just rechecked my math, and discovered something rather surprising that I'd overlooked. My apologies if it has been mentioned already, and my further apologies if I've made an error in my algebra.

We've talked about an apparent deflection that occurs when an object is dropped from a particular height. For example, an object dropped from a height of one meter above a floor that is 500 meters from the center of rotation will have an apparent deflection of about 4.225 cm.

If my math is right, the angular velocity of the wheel has nothing to do with the amount of deflection. Deflection is solely a function of (1) the "end" radius, i.e., the radius of the "floor" which the object eventually strikes, and (2) the "start" radius, which can be expressed in terms of the height from which the object is dropped.

In other words, it doesn't matter how fast the station is spinning (as long as it is spinning at some rate above zero radians per second). The amount of deflection would be the same.

For a centrifugal wheel such as the Discovery centrifuge in "2001," the amount of deflection of a falling object would be very pronounced, because the "end" radius is so small. If my calculations are right, and if I assume that the Discovery floor is ten meters from the center of rotation, dropping an object from one meter above the floor would produce a deflection of about one-third of a meter, which is very substantial.

[Johnny Pneumatic]

Read this (http://www.nasa.gov/vision/space/livinginspace/23jul_spin.html)

[Brown]

Originally posted by bewareofdogmas
Read this (http://www.nasa.gov/vision/space/livinginspace/23jul_spin.html) Pretty neat. The article suggests that it would not be unlikely that people would develop "space legs," akin to "sea legs." That is, they become accustomed to the environment. The might sense the station rotation at first, but they can adapt to it, and perhaps eventually become unaware of it.

It seems unlikely that they would become so accustomed that they would be able to play sports such as tennis, however. I expect that one would have to be on the space station for quite a while to get used to the way the ball bounces on both sides of the net (and if the space station is a resort, then such long stays would not be likely). Miniature golf would still be an option.

And of course, there would have to be zero-g games in the hub. I've developed a couple of such games. One of them has some similarity to baseball, in which players have to swat a foam ball with a hand, then float from "base" to "base" before the ball is retrieved by defenders. (In one varitation, there are four bases plus "home," arranged on the walls of the hub in a pentagram formation.) Another game is similar to the basketball-based game of "Horse," in which players try to hit a target with a ball while doing flips or other zero-g maneuvers.

Station personnel would be present as safety officers and as referees. Players would probably have to wear helmets, because of the ever-present possibility of inadvertent contact with other players. The walls of the hub would be heavily padded, and equipped with plenty of hand-holds. Ideally, the hub would not rotate with the station. (In addition to the recreational benefit, there are several practical reasons supporting non-rotation of the hub. For example, it can simplify the process of docking with spacecraft that ferry vacationers to and from the station. A pilot would not have to put his spacecraft into a roll, as depicted in the movie "2001." If memory serves, the "2001" novel described a hub that did not rotate during docking.)

[TeaBag420]

"A pilot would not have to put his spacecraft into a roll, as depicted in the movie "2001." If memory serves, the "2001" novel described a hub that did not rotate during docking.)"

So are you saying it did rotate or it didn't? And I'm not a pilot, but that's probably a spin, not a roll.

[Soapy Sam]

Brown- Niven has a new one out in the Ringworld Series- "Children of Ringworld". I read the intro only, in which he comments about the various "origins" and adaptations of the concept.

The Integral Trees I'm afraid baffled me utterly. I could not imagine the environment in which the action took place.