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Getting the Science Right, Part 2

Badly Shaved Monkey said:
(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.
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There is no difference in angular velocity between head and foot. There is a difference in linear velocity.
 
Badly Shaved Monkey said:
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.
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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.
 
SGT said:
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.
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I haven't verified the equation, but it seems a little high to me. The linear velocity would be V = ωr, and if the apparent acceleration is 2ωV, then the apparent acceleration would be 2ω<sup>2</sup>r. Since the radial acceleration is ω<sup>2</sup>r, 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.
 
Brown said:
I haven't verified the equation, but it seems a little high to me. The linear velocity would be V = ωr, and if the apparent acceleration is 2ωV, then the apparent acceleration would be 2ω<sup>2</sup>r. Since the radial acceleration is ω<sup>2</sup>r, 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.
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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.
 
Brown said:
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.
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I found 8.9924 days ~ 9 days, the same as you. The kinetic energy would be enormous.
 
wollery said:
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.
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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.
 
Let's see if I can attach the picture with the path viewed by the rotating observer.
 
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.
 
rppa said:
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.
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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.
 
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.
 
bewareofdogmas said:
Read this
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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.)
 
"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.
 
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.
 
Brown said:
Anybody want to do some computation about whether the gravity wheel would work? If so, take a look at Getting the Science Right.

At that size, it should be noted that, while there would be some sense of "gravity," objects are not going to fall "straight down." What will be perceived as tendency of objects to follow curved paths to the floor may have an effect upon several ordinary daily activites.
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Wow, this is an old thread.

Yes, an object dropped would appear to follow a curved path for the simple reason that anything at a "higher" point moves a little slower in its journey around the axis because that circle is a bit smaller than the circle formed by the floor in its journey around the axis. Further, the rate of fall would be at whatever the "gravity" effect the ball is experiencing at the moment it's dropped and would appear to accelerate only at that rate, where a similar ball that was "rolled" down a wall, if the wall were on the anti-spinward side of the ball, would appear to accelerate faster as it moved "down" because the wall would give it increased energy from the spin of the station.

Brown said:
Question 6: People on the Earth cannot "feel" the Earth rotating. Could people on the space station "feel" the station rotating?
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You would probably feel it while moving. Walking in the direction of the spin would increase the "gravity" force in you, but only while you're moving so the effect would go away the moment you stopped. By the same token, walking anti-spinward you would feel lighter, but only until you stopped.

Even more interesting than contemplating a dropped ball, I think, is contemplating a thrown ball. Throw it in the spinward direction and the ball appears to have an enhanced gravity effect, throw it anti-spinward and you may be able to achieve an anti-gravity effect for a while. Throw it perpendicularly to the direction of spin...and that, for me, is where imagining the arcs gets into brain-hurt territory.
 
Mycroft said:
Even more interesting than contemplating a dropped ball, I think, is contemplating a thrown ball. Throw it in the spinward direction and the ball appears to have an enhanced gravity effect, throw it anti-spinward and you may be able to achieve an anti-gravity effect for a while. Throw it perpendicularly to the direction of spin...and that, for me, is where imagining the arcs gets into brain-hurt territory.
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As I mentioned earlier in this old thread, I created a baseball-like zero-gravity game in which players can throw a ball to one another. This game would be played in a zero-gravity venue such as the hub of a rotating station. Throwing may take a bit of practice, as there might might be an unconscious tendency to throw high to overcome gravity. In the absence of gravity, the throw may sail over the intended recipient's head.

While on the rim of the station, though, throwing might be difficult for other reasons. Someone who is at a different place from you on the rim will seem to be above you, and you may have to compensate for that when you throw. If you're throwing to a person at the same place on the rim (but displaced from you laterally), you may see the ball curve to the right or the left.

In the case of the gravity wheel (on the "real" Enterprise), things get complicated even further, because the ship would be linearly accelerated and decelerated to get where it's going. (An orbiting space station, in contrast, is in free fall, and has little linear acceleration.) The experiences for those on the gravity wheel during linear acceleration or deceleration would be, I expect, unpleasant. The gravity wheel might only be habitable while the ship is "coasting," i.e., is undergoing no linear acceleration or deceleration.
 
Brown said:
I

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.
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S.F. Book illustrations in the 70's typically used windows to show scale of buildings & spacecraft.
 
Brown said:
In the case of the gravity wheel (on the "real" Enterprise), things get complicated even further, because the ship would be linearly accelerated and decelerated to get where it's going. (An orbiting space station, in contrast, is in free fall, and has little linear acceleration.) The experiences for those on the gravity wheel during linear acceleration or deceleration would be, I expect, unpleasant. The gravity wheel might only be habitable while the ship is "coasting," i.e., is undergoing no linear acceleration or deceleration.
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The "Build the Enterprise" website is wrong, I think, to try to make a real functioning Enterprise look like the one of fiction. A spinning wheel or disc for gravity, sure, but it needs to be perpendicular to the line of thrust.

To make the gravity wheel habitable during linear acceleration is an engineering problem easily solvable with today's' technology. You just need to think in terms of compartments that "float" in relation to an outer shell, with ballast to keep the floor oriented "down". Think of those novelty eyeballs that are sold around Halloween time where an eyeball always looks up from within a ball that's rolling across a table. Similar structures strung together like a necklace, only probably cylinders rather than spheres, make up the circle of your gravity ring. You could even vary the rotational speed of your ring to compensate for the added "gravity" of your thrust.
 
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