Getting the Science Right, Part 2

[wollery]

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]

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]

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]

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]

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]

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 2ωV, where ω is the angular velocity of the rotating frame and V is the linear velocity of the object.

 

[wollery]

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]

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]

#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]

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]

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]

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]

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]

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]

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]

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....

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.