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Yuggy
2009-Jul-22, 07:41 AM
I saw an interesting debate in the comments following the article on UniverseToday.com about building a Moon base.

http://www.universetoday.com/2008/03/22/building-a-base-on-the-moon-part-4-infrastructure-and-transportation/

One of the commentors stated the following "That same graceful push-off that initiates and sustains our walking gait on Earth will not work on a spinning space station or space craft. Once you impart enough energy to execute a normal step you overcome the artificial 1-g imparted by the angular momentum. Up you go and you are not coming back down. You're headed for the ceiling only to be bounced off if you can't grab anything to hold on."

I had never really thought about this before, so at first I gave some creedence to his logic. I quickly came to a conclusion that he was wrong.

If you jump up while spinning, you are actually jumping at a forward angle of momentum, and as the habitat spins beneath you, it changes direction. Soon your up and forward momentum is pointed towards the floor again and you fall to the ground. Infact it would simulate gravity almost perfectly. It has to, because the angles of trajectory and decent are constant in order to generate a 1 spin, regardless of size of the habitat.

Nevertheless, the poster did make me see a flaw. I think there are issues with artificial gravity caused by spinning.

Although the gravity would work perfectly if you were to jump in a 1G spin, your center of balance would be severely distorted if you were to make a full leap. Infact, if you were to jump high enough, you could feel as if you jumped straight up, and yet head towards the floor face first (belly smacker style, or back depending which way your facing).

Straight up is no longer straight up as the habitat spins. Its constantly changing. I can see serious issues caused by this problem. People may even have to get used to walking with a slightly backwards lean when they are traveling with this spin, and forward lean when they are traveling against it.

I've never read anything on this topic so if you guys have articles or comments discussing it, please post them.

G O R T
2009-Jul-22, 10:58 AM
Although the gravity would work perfectly if you were to jump in a 1G spin, your center of balance would be severely distorted if you were to make a full leap. Infact, if you were to jump high enough, you could feel as if you jumped straight up, and yet head towards the floor face first (belly smacker style, or back depending which way your facing).

Straight up is no longer straight up as the habitat spins. Its constantly changing. I can see serious issues caused by this problem. People may even have to get used to walking with a slightly backwards lean when they are traveling with this spin, and forward lean when they are traveling against it.


A centrifugal ring like the one in 2001 spins once in about 30 seconds. While you are in the air you would tend to spin at the ring habitat rotation rate, which could be corrected for only by estimation of "air time" and direction one is facing. Jogging would require both a spin correction according to direction, and an uphill correction in either direction to allow for curvature.

Still, it could be worse!

In a cylindrical spinning habitat you would have terrible coriolis effects while moving axially.

eburacum45
2009-Jul-22, 11:27 AM
Here's a good page about the differences between spin gravity and Earth gravity;
http://www.dyarstraights.com/msgundam/coriolis.html
I like the graphics showing the trajectory of a thrown ball. Juggling in a rotating habitat could be an interesting experience...

grant hutchison
2009-Jul-22, 01:30 PM
Another useful resource is Theodore Hall's Inhabiting Artificial Gravity (http://www.spacefuture.com/archive/inhabiting_artificial_gravity.shtml).

Grant Hutchison

Ken G
2009-Jul-22, 06:21 PM
A summary for those not looking up the links is that yes indeed, that "commentator" is talking complete nonsense. A good way to do calculations like this is to "enter the rotating frame", in which the ring seems stationary (which is also your own perspective if you are in it). To do this, you need to include two "non-inertial" forces, the centrifugal force (which will point "down" if you are standing there, and work virtually identically to normal gravity) and the coriolis force (which will point weakly up or down if you walk around the ring, or forward or backward if you jump up). I don't think there'll be any "uphill" correction to include if you just walk around, as you are not working against the centrifugal force. There shouldn't be too much problem with maintaining balance when you come back down from a jump, because all that will happen is you will be propelled slightly forward or slightly backward, but you can absorb that with a step upon landing, like stepping off a moving walkway.

tashirosgt
2009-Jul-23, 04:52 AM
Is it known yet how many hours per day future astronauts would have to spend in artificial normal gravity to avoid the ill effects of prolonged low gravity?

robross
2009-Jul-23, 04:59 AM
Babylon 5, that rare Scifi gem of a show that depicted (mostly) real world physics, had an episode in which this very issue came up.

The commander fell out of a moving train, in the center of the space station. He was in free fall, with a slow velocity approaching one of the walls of the (huge) space station. One character commented he'd be fine since he was weightless, but the other character pointed out that the walls of the space station, due to the size, were rotating around 60 mph, in order to keep the artificial gravity at 1G. So even though he was slowly drifting towards the wall, contact with the spinning floor would have killed him had not the Vorlons intervened.

Rob

timb
2009-Jul-23, 09:19 AM
A summary for those not looking up the links is that yes indeed, that "commentator" is talking complete nonsense. A good way to do calculations like this is to "enter the rotating frame", in which the ring seems stationary (which is also your own perspective if you are in it). To do this, you need to include two "non-inertial" forces, the centrifugal force (which will point "down" if you are standing there, and work virtually identically to normal gravity) and the coriolis force (which will point weakly up or down if you walk around the ring, or forward or backward if you jump up). I don't think there'll be any "uphill" correction to include if you just walk around, as you are not working against the centrifugal force. There shouldn't be too much problem with maintaining balance when you come back down from a jump, because all that will happen is you will be propelled slightly forward or slightly backward, but you can absorb that with a step upon landing, like stepping off a moving walkway.

I seem to recall a third non-inertial force that only manifests itself when accelerating (wrt the local non-inertial frame). All the unwanted forces are mitigated by making the radius of revolution bigger. The usual model is a huge ring or even more ambitious Rama-like cylinder. A cheaper design might be something like skylab attached to a counterweight (such as a nuclear reactor) by a very strong cable.

tnjrp
2009-Jul-23, 09:42 AM
"Guess kids these days just can't tell their gravity from their rotating frame of reference"
~ Iain M. Banks, "Consider Phlebas"

Ken G
2009-Jul-23, 02:37 PM
I seem to recall a third non-inertial force that only manifests itself when accelerating (wrt the local non-inertial frame).You are probably thinking of a third non-inertial force that appears if the rotation of the frame of reference accelerates, not if the body being analyzed accelerates. The rotating space station will have a constant rotation rate, so no third force appears.

grant hutchison
2009-Jul-23, 04:05 PM
The commander fell out of a moving train, in the center of the space station. He was in free fall, with a slow velocity approaching one of the walls of the (huge) space station. One character commented he'd be fine since he was weightless, but the other character pointed out that the walls of the space station, due to the size, were rotating around 60 mph, in order to keep the artificial gravity at 1G. So even though he was slowly drifting towards the wall, contact with the spinning floor would have killed him had not the Vorlons intervened.I never found Babylon 5 particularly watchable, but if I recall correctly the habitat looked like a Bernal sphere. So I'm imagining the commander was falling through the air of the habitat, rather than through vacuum.
If that's so, then air drag would have had an effect. As the commander moved radially outwards from the central axis, he would have experienced a "wind" blowing in the spinward direction. That would have gently accelerated him spinwards, while Coriolis deflected him towards the floor of the habitat. The net effect would be a tendency to match the transverse speed of the habitat floor, while accelerating towards it. The final impact would therefore have both tangential and radial components, as quite a complicated function of the size and rotation speed of the habitat, the resulting gradient in air density, and the commander's coefficient of drag.

Of course, if this all took place in some central vacuum region, then everything I've said is irrelevant. :)

Grant Hutchison

publius
2009-Jul-23, 04:27 PM
You are probably thinking of a third non-inertial force that appears if the rotation of the frame of reference accelerates, not if the body being analyzed accelerates. The rotating space station will have a constant rotation rate, so no third force appears.

Yep. We can derive the Coriolis frame forces from the following operator relation.

d/dt (inertial) = [d/dt + w x]

Applying that twice for the acceleration we have, and taking care with our vector product derivative rules:

[d/dt + w x]*[d/dt + w x] =

[d^2/dt^2 + dw/dt x + w x d/dt + w x d/dt + w x w x] =

[d^2/dt^2 + 2w x d/dt + w x w x + dw/dt x]

Apply that to the position vector and we can thus read off the "gravity":

-w x w x r = centrifugal ("gravitoelectric") (scalar magnitude w^2r]

-2w x dr/dt = 2w x v = coriolis force ("gravitomagnetic")

-dw/dt x r = "third force" present only when w is not constant. And note this would be gravitoelectric like, not velocity dependent, at least in the Newtonian limit. (what this would be in the full "R" treatment, I have no idea, but it would be more complicated, I'm sure)

-Richard

Ken G
2009-Jul-23, 04:34 PM
So I'm imagining the commander was falling through the air of the habitat, rather than through vacuum. If that's so, then air drag would have had an effect.Good point. I believe the terminal speed of a man who wants maximum wind resistance is about 100 mph, very roughly, so 60 mph certainly creates a significant acceleration, of order a half a g or some such thing. Since the wind was usually less, maybe he'd feel an average acceleration of about g/10, very roughly. or 8000 miles per hour squared. So the scale of the time to approach 60 mph is on the order of a minute, and I presume the incident played out on a much longer time. So yes, the whole incident was physically quite bogus, you're right-- he would not have been in any danger.

grant hutchison
2009-Jul-23, 05:54 PM
So yes, the whole incident was physically quite bogus, you're right-- he would not have been in any danger.I think he was in danger, just a different danger. By making him participate in the general rotation of the habitat, the air drag exposes our falling commander to the centrifugal pseudoforce: he accelerates all the way to the "floor", from the rotating point of view of those within the habitat.
His impact would still have been violent, but directed more "vertically" than "horizontally" (radial rather than tangential).

Grant Hutchison

NEOWatcher
2009-Jul-23, 06:20 PM
Good point. I believe the terminal speed of a man who wants maximum wind resistance is about 100 mph, very roughly, so 60 mph certainly creates a significant acceleration, of order a half a g or some such thing.
Wind resistance computed into g?

So; I'm not going to go sliding along the concrete at any where near 60 miles an hour if I fell of the roof of a truck?

I'm not trying to say it doesn't have an effect, or even little effect, just that I don't see terminal velocity to be a formula with g. It's an intersection point with two formulas, one with g and the other with resistance.

grant hutchison
2009-Jul-23, 06:41 PM
I'm not trying to say it doesn't have an effect, or even little effect, just that I don't see terminal velocity to be a formula with g. It's an intersection point with two formulas, one with g and the other with resistance.It's a balance of forces. In the case of falling through air on Earth, one of the forces is gravity, and the other is generated by the pressure drop across the falling object, which scales roughly as velocity squared for turbulent flow. The balance at 100mph for a human tells us that a 100mph wind exerts the same force as gravity. From that, and the rough scaling, we know that a 60mph wind will apply a force to the same human equivalent to about 1/3g.
Unfortunately, during your fall from the roof of a truck you won't experience that force for long enough for it to seriously modify your velocity when you hit the ground. You will, however, notice that you don't fall in a perfectly vertical line relative to the moving truck. And if you were to fall far enough, your tranverse velocity would be effectively damped away by wind resistance: which is why small meteorites all arrive at ground level falling essentially vertically at their terminal velocity.

Grant Hutchison

NEOWatcher
2009-Jul-23, 06:46 PM
Unfortunately, during your fall from the roof of a truck...
Yeah, that's why I qualified my post. That was a quite extreme visual to make.
Your explanation makes sense, but there's an additional factor in this discussion that you would need to add. The wind will not be as strong the farther you get from the floor.

grant hutchison
2009-Jul-23, 06:51 PM
Yeah, that's why I qualified my post. That was a quite extreme visual to make.
Your explanation makes sense, but there's an additional factor in this discussion that you would need to add. The wind will not be as strong the farther you get from the floor.Yes, Ken tried to allow for that, to an order of magnitude, by cutting the acceleration to 1/10g. It's just a way of saying that wind resistance is a significant player if the velocity of prime interest is 60mph (rotation velocity of the floor) and the scenario plays out over many minutes.
In fact, our falling human would just be constantly nudged to match the angular velocity of the habitat by a gentle relative wind blowing towards spinwards, all the way from near-axis to floor. To someone rotating with the habitat, his Coriolis deflection to antispinwards would be constantly damped by wind resistance.

Grant Hutchison

publius
2009-Jul-23, 07:08 PM
This reminds me of some excercises we had to do way back in my Mechanics course -- projectile motion.

When you add air resistance, the equations of motion become more complicated, but still solvable analytically (assuming some simple air resistance function). Rather than a parabola, the trajectory becomes a logarimithic curve, with a vertical drop at the end as the horizontal velocity asymptotically goes to zero.

With a simple parabolic trajectory, the maximum range occurs when the projecticle is fired at a 45 degree angle, but that is modified with air resistance.

Now, if you take into account the variation of air density with height, the equations have no closed form solution IIRC, but here maximum range can be at greater than a 45 degree angle as if you get it high enough, the lesser air resistance more than makes up for the loss of initial horizontal velocity.

We then added the coriolis forces of the earth's rotation into the mix and had decide under what ranges and conditions that would become significant. IIRC, for long range artillery, like the big 16" guns on battleships with ranges of 20 miles or more, it does become significant.

And then I recently bought myself a new rifle, a DPMS LR-308 which is basically an AR-15 that shoots .308s, and had to refamiliarize myself with rifle ballistics to get the scope zeroed. The "logarithmic" character of the trajectory is noticeable over the bullet's useful range with the drop at the end sharper than parabolic.

The line of sight will intersect the trajectory in two spots (unless your zero happens to be exactly at the vertex of the trajectory :) ) and for this combination, a far zero at 200 yards has a near zero at 30, and thus I zeroed at 30.

-Richard

NEOWatcher
2009-Jul-23, 07:20 PM
Yes, Ken tried to allow for that, to an order of magnitude, by cutting the acceleration to 1/10g.
I see...
But the scene is wrong anyway as you have previously mentioned.
In my words, the wind would cause him to accelarate to the floor and go splat (or at least, thud).

robross
2009-Jul-23, 07:33 PM
I see...
But the scene is wrong anyway as you have previously mentioned.
In my words, the wind would cause him to accelarate to the floor and go splat (or at least, thud).

I think he's saying the scene is wrong because he would NOT go splat.

In the scene, he's basically in free fall, though not moving with any great velocity. But the tension in the scene is created by explaining that eventually he'll float to the interior side of the rotating cylinder, which would presumably kill him since he would impact it with a tangential (horizontal) velocity of 60mph.

But I think Grant is saying that the wind caused by the rotation would in fact accelerate the commander in the direction of the spin, thus he would actually impact with a horizontal velocity of 60mph, thus he would just land softly in place.

Rob

Ken G
2009-Jul-23, 07:34 PM
I think he was in danger, just a different danger. By making him participate in the general rotation of the habitat, the air drag exposes our falling commander to the centrifugal pseudoforce: he accelerates all the way to the "floor", from the rotating point of view of those within the habitat.
His impact would still have been violent, but directed more "vertically" than "horizontally" (radial rather than tangential).
This is an interesting question. Thinking about it, I could not convince myself of a way to estimate the magnitude of this effect. I agree it will be some fraction of 60 mph, but if it's 30 mph we have a splat, and if it's 15 mph we have a broken ankle on an embarrassed commander. Which is it going to be? Probably requires a full calculation, these parameters place it pretty much in the "hard to guess" realm. Still, if I had to, I'd put myself in the "broken ankle" camp, or maybe no injury at all. I can't see the need for Vorlon intervention with these parameters, but a full calculation might surprise me!

grant hutchison
2009-Jul-23, 07:57 PM
But I think Grant is saying that the wind caused by the rotation would in fact accelerate the commander in the direction of the spin, thus he would actually impact with a horizontal velocity of 60mph, thus he would just land softly in place.Ken was saying that, in his first post on the subject.
I'm concerned that, by nudging the commander to corotate with the habitat, the wind resistance makes him susceptible to centrifugal pseudoforce. From the rotating point of view of those in the habitat, he's going to experience an acceleration towards the "floor". As Ken says, the magnitude of that acceleration is rather difficult to estimate, since it depends on how much he lags behind the general rotation.
I did some simulations of this once, but it was more than twenty years ago, inspired by a similar scenario in one of John Varley's "Titan" novels. I recall the "vertical" impact velocity got to be quite significant under some circumstances, but I couldn't now say what those were.

Grant Hutchison

grant hutchison
2009-Jul-23, 08:07 PM
This is an interesting question. Thinking about it, I could not convince myself of a way to estimate the magnitude of this effect. I agree it will be some fraction of 60 mph, but if it's 30 mph we have a splat, and if it's 15 mph we have a broken ankle on an embarrassed commander. Which is it going to be? Probably requires a full calculation, these parameters place it pretty much in the "hard to guess" realm. Still, if I had to, I'd put myself in the "broken ankle" camp, or maybe no injury at all. I can't see the need for Vorlon intervention with these parameters, but a full calculation might surprise me!Yes, depending on the parameters, one might be able to manage the situation by driving a flat-bed truck at an appropriate speed, with a small team of people in the back holding a catching blanket. :)
I'd personally pay to watch that, rather than a Vorlon intervention (he says, having no idea what a Vorlon intervention might involve).

Grant Hutchison

Ken G
2009-Jul-23, 08:20 PM
Yes, depending on the parameters, one might be able to manage the situation by driving a flat-bed truck at an appropriate speed, with a small team of people in the back holding a catching blanket. Now there would be a fitting calculation for a spaceborne crew, to figure out the required motion of that truck! (Also, a nice high ladder might help with the final stages of the acceleration, which are likely the worst-- I get the radius must be about 35 meters, so a 10-meter ladder would sure take the sting out). All that would be more believable than the usual sci fare fare, "if we could just reverse the polarity of the tachyon impulse generator..."


I'd personally pay to watch that, rather than a Vorlon intervention (he says, having no idea what a Vorlon intervention might involve).
I think I saw it in a reality show at one point. :)

robross
2009-Jul-23, 08:30 PM
Yes, depending on the parameters, one might be able to manage the situation by driving a flat-bed truck at an appropriate speed, with a small team of people in the back holding a catching blanket. :)
I'd personally pay to watch that, rather than a Vorlon intervention (he says, having no idea what a Vorlon intervention might involve).

Grant Hutchison

Well flatbed trucks were hard to come by, and also there were no real roads for them to drive on, if they were available. :)

But as for what the Vorlon intervention entailed, there's a picture of it on the wiki page for this particular episode:

http://en.wikipedia.org/wiki/The_Fall_of_Night

Rob

Glom
2009-Jul-23, 08:30 PM
If the radius of the habitat is small, then everything is truly screwed up. If it's a bit big, then you have gravity but with complications. Moving along the axis of rotation, it seems normal. Moving in the direction of rotation, you feel heavier, while you feel lighter moving in the opposite direction. Moving axially, you start to get coriolis force pushing you forward and backward.

If the habitat is huge, then these effects aren't very noticeable.

Grashtel
2009-Jul-23, 09:53 PM
This is an interesting question. Thinking about it, I could not convince myself of a way to estimate the magnitude of this effect. I agree it will be some fraction of 60 mph, but if it's 30 mph we have a splat, and if it's 15 mph we have a broken ankle on an embarrassed commander. Which is it going to be? Probably requires a full calculation, these parameters place it pretty much in the "hard to guess" realm. Still, if I had to, I'd put myself in the "broken ankle" camp, or maybe no injury at all. I can't see the need for Vorlon intervention with these parameters, but a full calculation might surprise me!
The question is what will be his vertical speed? The station is IIRC about a kilometre in diameter so if he reaches a stop relative to the air too high he may actually hit faster than 60mph because he has been free falling for several hundred meters.

grant hutchison
2009-Jul-23, 10:16 PM
The question is what will be his vertical speed? The station is IIRC about a kilometre in diameter so if he reaches a stop relative to the air too high he may actually hit faster than 60mph because he has been free falling for several hundred meters.60mph at such a radius gives under a seventh of a gravity. Perhaps the originally stated velocity was 160mph? That would provide 1g at a radius of 500m.

Grant Hutchison

Ken G
2009-Jul-23, 10:19 PM
Moving axially, you start to get coriolis force pushing you forward and backward.This is the second time in this thread I've heard this idea expressed, but I'm not sure where it is coming from, because motion in the direction of the axis of rotation does not experience any coriolis effects.


If the habitat is huge, then these effects aren't very noticeable.To maintain g at the rim, you find that the rotation rate (i.e., frequency) must scale inverse to the square root of the radius. This also means that the speed of the rim, relative to the center, scales like the square root of the radius. So whether or that is noticeable as the habitat gets huge depends on if you are talking about instantaneous effects, like coriolis accelerations, or effects that are integrated over the motion, like the commander's predicament in the OP. For a much larger habitat, he'd be in deep trouble.

Ken G
2009-Jul-23, 10:23 PM
60mph at such a radius gives under a seventh of a gravity. Perhaps the originally stated velocity was 160mph? That would provide 1g at a radius of 500m.
Yeah, I got a habitat radius of 36 m would give one g with 60 mph. That does seem like a pretty small habitat given that pic on the web, so I'm thinking the 60 mph number was too low. In that case, the commander is indeed in trouble, even with the wind resistance helping him out.

Ken G
2009-Jul-23, 10:25 PM
The question is what will be his vertical speed? The station is IIRC about a kilometre in diameter so if he reaches a stop relative to the air too high he may actually hit faster than 60mph because he has been free falling for several hundred meters.It's impossible for him to hit with a speed above the airspeed (which is also the rimspeed), a fact that is clear if you consider only the nonrotating frame.

grant hutchison
2009-Jul-23, 10:30 PM
This is the second time in this thread I've heard this idea expressed, but I'm not sure where it is coming from, because motion in the direction of the axis of rotation does not experience any coriolis effects.I think by "axially" Glom means "radially": towards or away from the axis, rather than parallel to the axis.

Grant Hutchison

grant hutchison
2009-Jul-23, 10:38 PM
Yeah, I got a habitat radius of 36 m would give one g with 60 mph.One of us is out by a factor of two. I'm getting 73m. Still, much smaller than Babylon 5 seems to be.

Grant Hutchison

Ken G
2009-Jul-23, 10:41 PM
One of us is out by a factor of two. I'm getting 73m. Still, much smaller than Babylon 5 seems to be.
You're quite right, I mistook a radius for a diameter. It's 73 m, and yes, that doesn't seem right, so it must be much faster than 60 mph-- and the "ladder" idea isn't going to do much. Also, the commander is toast-- if not for the Vorlon angel thingy. (Personally, I quite liked the political intrigue in B5, it was a step up from the black-and-white win-the-fistfight fare we used to get in sci fi before B5 raised the bar. I won't speak for their science though...)

grant hutchison
2009-Jul-23, 10:52 PM
Personally, I quite liked the political intrigue in B5, it was a step up from the black-and-white win-the-fistfight fare we used to get in sci fi before B5 raised the bar.I'm sure it was. I just have an inability to track dialogue when too many of the actors involved are wearing plastic heads. It's a significant disability, which I acknowledge but don't seem to be able to do anything about. It's been undermining my viewing pleasure since William Hartnell (http://www.scifiscience.co.uk/img/drwho/William_Hartnell.jpg) was Doctor Who and Jonathan Harris (http://s3.amazonaws.com/findagrave/photos/2002/312/6905115_1036826259.jpg) was Doctor Smith.

Grant Hutchison

G O R T
2009-Jul-23, 11:05 PM
This is the second time in this thread I've heard this idea expressed, but I'm not sure where it is coming from, because motion in the direction of the axis of rotation does not experience any coriolis effects.


Some amusement houses have a rotating tube to walk through.
What would be the name for this disorienting situation?

grant hutchison
2009-Jul-23, 11:42 PM
It's impossible for him to hit with a speed above the airspeed (which is also the rimspeed), a fact that is clear if you consider only the nonrotating frame.Like the professor in the joke, I've just had to do the maths to be sure that this was intuitively obvious. :lol:

If the commander falls radially outwards (say, he's constrained by a frictionless radial rail, rather than wind resistance), he takes the full hit of the centrifugal pseudoforce, all the way to the rim.
For a given habitat angular velocity ω, his acceleration at radius r is ωr.
Assuming a starting velocity of zero, we can integrate to get radial velocity as a function of radius:

v = 2ω∫r dr

For a fall from the axis (r = 0) to the rim (r = R) we get:

v = ωR

But ωR is just the rim speed. So in the rotating frame our radially-constrained commander, falling all the way from the axis under centrifugal "gravity", strikes the rim vertically with a velocity equal to rim speed.
(Notice he'll need an infinitesimal nudge off-axis if he is to make the journey in a finite time.)

Grant Hutchison

Ken G
2009-Jul-24, 05:16 AM
Some amusement houses have a rotating tube to walk through.
What would be the name for this disorienting situation?That's quite a different kettle of fish, because you also have regular gravity in that situation.

Ken G
2009-Jul-24, 05:28 AM
Like the professor in the joke, I've just had to do the maths to be sure that this was intuitively obvious.Yeah, what is "obvious" is not necessarily obvious! I once had a friend of mine field a criticism at the end of his talk that went something like "But what you are saying is perfectly obvious, and what's more, I'm not even sure it's true."


If the commander falls radially outwards (say, he's constrained by a frictionless radial rail, rather than wind resistance), he takes the full hit of the centrifugal pseudoforce, all the way to the rim.Here's another way-- if all forces but centrifugal are cancelled out, you can use the fact that the centrifugal force comes from a conservative potential in the rotating frame. Then the magnitude of the velocity, in the rotating frame, comes from conservation of energy. Note that this generalizes, because both the coriolis force and any frictionless rail will act perpendicular to the motion, so neither ever does any work, so neither alter the speed in the rotating frame. So in the absence of air resistance, if he slides along a frictionless rail of any geometry, he always hits at the rim speed, in the rotating frame. We just don't know from which direction he hits the rim until we know the geometry of the rail.

If you put in air resistance, it will always dissipate energy into heat. Hence he can never have more kinetic energy with the air there than he would have without it. So this is a proof that works in the rotating frame. In the non-rotating frame, it seemed to make sense, but I can't prove it in that frame, so I think it wasn't obvious after all!

grant hutchison
2009-Jul-24, 10:21 AM
If you put in air resistance, it will always dissipate energy into heat. Hence he can never have more kinetic energy with the air there than he would have without it.So with that, and our realization that (in the Babylon 5 scenario) the rim speed is probably uncomfortably higher than the commander's terminal velocity at STP and 1g, it seems likely he's going to hit the floor at something pretty close to the local terminal velocity. We're just not sure of how that velocity will be distributed into radial and tangential components at the moment of impact.

Grant Hutchison

tnjrp
2009-Jul-24, 11:27 AM
Generally speaking, while you can count on B5 to make a mess of details of the specific science (they did that quite often enough -- tho it's more of a "based on real science" type of show than most of the competitors) I'm fairly certain Sheridan wouldn't have needed to go to Zha'ha'dum to die if Kosh or somebody else wouldn't have played catch with him there in the centeral cylinder :shifty:

Brutal Mustang
2009-Jul-24, 11:40 AM
I was searching for a thread like this 2 days ago, and couldn't find any. What I want to know is if someone threw a ball up towards the axis of such a gravity cylinder, would it stay up there floating around?

grant hutchison
2009-Jul-24, 12:48 PM
I was searching for a thread like this 2 days ago, and couldn't find any. What I want to know is if someone threw a ball up towards the axis of such a gravity cylinder, would it stay up there floating around?Only if its trajectory were precisely tailored to be the opposite of the same ball if it fell from rest on the axis. If not, the ball would appear to follow a curving trajectory (as seen by observers rotating with the habitat) which either missed or passed through the axis line and then fell back to the floor again.
Even if you placed something very precisely at the axis of an air-filled habitat, it would soon be displaced by random air currents. And once off-axis, it would eventually fall.

It's a little like trying to balancing a pencil on its point (or, in the case of the thrown ball, of throwing a pencil to balance on its point). Theoretically possible, but not practically stable.

Grant Hutchison

Ken G
2009-Jul-24, 01:04 PM
So with that, and our realization that (in the Babylon 5 scenario) the rim speed is probably uncomfortably higher than the commander's terminal velocity at STP and 1g, it seems likely he's going to hit the floor at something pretty close to the local terminal velocity. We're just not sure of how that velocity will be distributed into radial and tangential components at the moment of impact.That seems like a fine deduction, at least in terms of a good way to approximate the scale of his speed. Note that strictly speaking, the concept of terminal speed requires that the acceleration be consistent at 1 g, and point in the same direction as the motion. So we have a few details that we can't get to behave, but it may work out that the speed cannot exceed the terminal speed, given the small speed he starts with, and is likely approximated by that scale, but I believe the more tangential is his final speed, the more he can be slowed below the terminal speed (i.e., the terminal speed would use only the component of 1 g that lies along the final direction). I certainly think he's in deep trouble if the rim speed is, as we have determined, much faster than 60 mph, because even a component of the terminal speed would be pretty deadly.

Glom
2009-Jul-24, 07:16 PM
Yes, I meant radially. My bad. :doh:

Brutal Mustang
2009-Jul-24, 09:55 PM
It's a little like trying to balancing a pencil on its point (or, in the case of the thrown ball, of throwing a pencil to balance on its point). Theoretically possible, but not practically stable.

Grant Hutchison

Fascinating. Thanks, Grant!

grant hutchison
2009-Jul-24, 10:38 PM
Fascinating. Thanks, Grant!Pleasure. :)

Grant Hutchison

matthewota
2009-Jul-28, 03:55 PM
In a spinning habitat, wouldn't your inner ear balance get messed up from the rotational forces? I recall being in a carnival ride when I was a teenager. It was the spinning cylinder that pinned you up against the wall and then the floor dropped. When I turned my head to the side I got very dizzy.

grant hutchison
2009-Jul-28, 04:19 PM
In a spinning habitat, wouldn't your inner ear balance get messed up from the rotational forces? I recall being in a carnival ride when I was a teenager. It was the spinning cylinder that pinned you up against the wall and then the floor dropped. When I turned my head to the side I got very dizzy.There's been quite a lot of work done on this. If the rotation rate is less than one revolution per minute, Coriolis effects on the inner ear seem to be well tolerated, especially after adaptation.
A quotation from my earlier link (http://www.spacefuture.com/archive/inhabiting_artificial_gravity.shtml):
In brief, at 1.0 rpm even highly susceptible subjects were symptom-free, or nearly so. At 3.0 rpm subjects experienced symptoms but were not significantly handicapped. At 5.4 rpm, only subjects with low susceptibility performed well and by the second day were almost free from symptoms. At 10 rpm, however, adaptation presented a challenging but interesting problem. Even pilots without a history of air sickness did not fully adapt in a period of twelve days.
Grant Hutchison

robross
2009-Jul-28, 06:06 PM
There's been quite a lot of work done on this. If the rotation rate is less than one revolution per minute, Coriolis effects on the inner ear seem to be well tolerated, especially after adaptation.
A quotation from my earlier link (http://www.spacefuture.com/archive/inhabiting_artificial_gravity.shtml):
Grant Hutchison

Wouldn't this depend on the radius of the rotating cylinder? The longer the radius, the faster the outer wall of the cylinder is moving. So 1 rpm for a sufficiently large radius could represent a tremendous velocity and centripetal force.

Rob

grant hutchison
2009-Jul-28, 06:22 PM
Wouldn't this depend on the radius of the rotating cylinder? The longer the radius, the faster the outer wall of the cylinder is moving. So 1 rpm for a sufficiently large radius could represent a tremendous velocity and centripetal force.The effect on your inner ear depends on the angular velocity (how many times a minute your head rotates). As you say, bigger habitats will give you the same force for a lower rotation rate, so they can provide adequate centrifugal gravity at a lower rotatiion rate, and therefore with less of hit on your inner ear.

Grant Hutchison

Glom
2009-Jul-28, 09:05 PM
Coriolis acceleration = v w

So it the fritzing of the inner ear would be related to the angular velocity.

Since Centripetal acceleration = wr, a larger radius will deliver the desired gravity for a lower angular speed so Coriolis force is less.

So if you had a massive space station spinning at 1pm, you wouldn't get dizzy, you'd just be crushed into jelly.

Ken G
2009-Jul-28, 10:15 PM
Coriolis acceleration = v wNot that is matters, but you forgot a factor of 2.