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Rendezvous with Rama



 
 
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  #1  
Old March 25th 04, 05:13 PM
Richard Cavell
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Default Rendezvous with Rama

I'm reading this book by Arthur C. Clarke. It involves a spaceship of
sorts, which is a cylinder that rotates about its long axis. The idea is
that a person standing on the inside of the cylinder will experience a
pseudo-'gravity' in the form of a centripetal force that pushes his feet up.
I have a few concerns with this, which are probably relevant to any such
device engineered to create 'gravity' this way.

1. If I'm standing on the inside surface of the cylinder and I jump up,
there is no true 'pull' on me that accelerates me toward the 'floor' like
there is with real gravity. Consequently, if I jump, I will simply float up
and through the long axis, to the other side of the cylinder.

A natural consequence of this is that I can't run on the floor, since this
involves both my feet leaving the floor and not touching again till I hit
the other side. If I fell asleep an area with no roof, I could float away
if I were not strapped down.

2. Also, imagine I were standing on the floor of this cylinder facing the
direction in which it turns. The ground and I are travelling in that same
direction, so I appear to be stationary. However, the ground also slowly
moves 'up' in front of me and also rotates my body 'backwards' slightly.
This would mean that every time I jump I would appear to somersault slightly
in the direction of turn, or alternatively if I turned around 180 degrees, I
would appear to somersault slightly backwards when I jump (or even just
standing there).

This would mean that whatever angle I stand at, my postural reflexes will
have to alter slightly on two sides of my body and I will easily tell which
way the ground am turning.

3. Arthur C Clarke supposes that the air is denser toward the 'floor' than
toward the middle of the cylinder.

This doesn't seem right at all. There is nothing attracting the air to the
floor. Surely the air might be caused to rotate slightly because of the
friction between the floor and the outermost laminar layer, but that would
not be transferred to all the other air molecules. Air is 'slippery' enough
that even two metres above the floor I'd imagine that it would be relatively
motionless and that the gas would evenly distribute itself throughout the
rest of the cylinder.

This means that if I'm standing on the floor, I will feel a breeze.

Am I right in all this?



  #2  
Old March 26th 04, 07:45 AM
Mb
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Default Rendezvous with Rama

On Fri, 26 Mar 2004 03:13:21 +1100, "Richard Cavell"
wrote:

I'm reading this book by Arthur C. Clarke. It involves a spaceship of
sorts, which is a cylinder that rotates about its long axis. The idea is
that a person standing on the inside of the cylinder will experience a
pseudo-'gravity' in the form of a centripetal force that pushes his feet up.
I have a few concerns with this, which are probably relevant to any such
device engineered to create 'gravity' this way.

1. If I'm standing on the inside surface of the cylinder and I jump up,
there is no true 'pull' on me that accelerates me toward the 'floor' like
there is with real gravity. Consequently, if I jump, I will simply float up
and through the long axis, to the other side of the cylinder.

A natural consequence of this is that I can't run on the floor, since this
involves both my feet leaving the floor and not touching again till I hit
the other side. If I fell asleep an area with no roof, I could float away
if I were not strapped down.


If you're standing inside a rotating cylinder, you're moving with that
rotation. If you jumped "up", your body would move in a straight line,
but that line would be a combination of the rotation motion, deflected
slightly by your jumping action. Since the larger motion would be the
rotation, your net direction of movement would not be toward the
center axis of the cylinder. It would instead be back to the cylinder
surface a bit further along in its rotation. It would feel exactly
like jumping up and falling back down.

2. Also, imagine I were standing on the floor of this cylinder facing the
direction in which it turns. The ground and I are travelling in that same
direction, so I appear to be stationary. However, the ground also slowly
moves 'up' in front of me and also rotates my body 'backwards' slightly.
This would mean that every time I jump I would appear to somersault slightly
in the direction of turn, or alternatively if I turned around 180 degrees, I
would appear to somersault slightly backwards when I jump (or even just
standing there).

This would mean that whatever angle I stand at, my postural reflexes will
have to alter slightly on two sides of my body and I will easily tell which
way the ground am turning.


Rama is something like 20 km across. In such a large vessel, the
difference in the speed of rotation between your head and your feet
would be negligible.

3. Arthur C Clarke supposes that the air is denser toward the 'floor' than
toward the middle of the cylinder.

This doesn't seem right at all. There is nothing attracting the air to the
floor. Surely the air might be caused to rotate slightly because of the
friction between the floor and the outermost laminar layer, but that would
not be transferred to all the other air molecules. Air is 'slippery' enough
that even two metres above the floor I'd imagine that it would be relatively
motionless and that the gas would evenly distribute itself throughout the
rest of the cylinder.

This means that if I'm standing on the floor, I will feel a breeze.


Nope. Although it's true that when Rama was first "spun up", the air
would have lagged behind the rest of the vessel, friction between the
air, and all of Rama's interior surfaces, would eventually cause the
air volume to rotate as well. Keep in mind that there's nothing in
Rama which _isn't_ rotating. And once the air volume is set in
rotation, it would tend to push outward.

Mike
--
Mb / -==0 @
/ A
/ C3==# / \
  #3  
Old March 27th 04, 12:39 AM
Keith Harwood
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Posts: n/a
Default Rendezvous with Rama

Richard Cavell wrote:

I'm reading this book by Arthur C. Clarke. It involves a spaceship of
sorts, which is a cylinder that rotates about its long axis. The idea is
that a person standing on the inside of the cylinder will experience a
pseudo-'gravity' in the form of a centripetal force that pushes his feet
up. I have a few concerns with this, which are probably relevant to any
such device engineered to create 'gravity' this way.

1. If I'm standing on the inside surface of the cylinder and I jump up,
there is no true 'pull' on me that accelerates me toward the 'floor' like
there is with real gravity. Consequently, if I jump, I will simply float
up and through the long axis, to the other side of the cylinder.


Nope. Don't forget, when you are standing still on the floor you are still
revolving around the axis. When you jump up you are no longer being acted
upon by a force therefore you continue moving in a straight line in the
direction which is the sum of your tangential velocity at the moment you
left the floor plus the tiny extra from your jump. You are travelling in a
straight line, but the floor is curving up to meet you, so you hit it
pretty soon after. And since you are moving in a straight line at pretty
much the same speed that the floor is moving in its circle and in the same
direction you are going to hit pretty much the same piece of floor you
started off from. In other words, it's pretty much like jumping in a
gravity field.

A natural consequence of this is that I can't run on the floor, since this
involves both my feet leaving the floor and not touching again till I hit
the other side. If I fell asleep an area with no roof, I could float away
if I were not strapped down.


Nope, it's pretty much like running on earth. Every time you leave the floor
it curves round to meet you. The main difference is that when you run to
spinward you are adding your running velocity to the floor's tangential
velocity so you meet the floor rather sooner, when you are running
anti-spinwards you are subtracting it and meet te floor rather later. So
running to spinward is a bit like running up hill, anti-spinward is like
down hill. If you could run anti-spinward at the floor's tangential
velocity, then you would just float, but at that speed you are likely to
break a number of world records.

2. Also, imagine I were standing on the floor of this cylinder facing the
direction in which it turns. The ground and I are travelling in that same
direction, so I appear to be stationary. However, the ground also slowly
moves 'up' in front of me and also rotates my body 'backwards' slightly.


Nope. This would happen only when the the cylinder started spinning. If it
is at constant speed then so are you and there's no net force making you
tilt.

Standing still is not a problem, so long as you keep your head still. At the
size the Rama is, you don't even have the ear canal problem, that's only on
much smaller structures.

However, there is a problem best illustrated with ladders (or the stairs in
the endcap, but let's just consider a ladder going straight up from the
floor). The tangential velocity of the bottom of the ladder is the same as
the floor. The velocity at the top (at the axis) is zero. So if you climb
the ladder it will be pushing back at you trying to slow you down. If you
are climbing on the anti-spinward side it would feel like the ladder was
curving over on top of you. Climbing on the other side would feel like it
was curving away from you. Coming down would be the opposite.

3. Arthur C Clarke supposes that the air is denser toward the 'floor'
than toward the middle of the cylinder.

This doesn't seem right at all. There is nothing attracting the air to
the
floor. Surely the air might be caused to rotate slightly because of the
friction between the floor and the outermost laminar layer, but that would
not be transferred to all the other air molecules.\


Yes it would be. There is nothing to stop the air turning so when the
cylinder started spinning it would keep on doing so. And, don't forget,
when they first arrive all the air is on the floor, frozen, and therefore
turning. As it evaporates it keeps on turning because there is nothing to
stop it. (That's very rough. More strictly, each molecule travels in a
straight line until it hits something. Usually it's another molecule, but
because the floor curves up to meet the molecules quite a lot more are
going to hit it if they are close to it than if they were far away. In
other words, the density of molecules is going to be greater near the
floor.)

Air is 'slippery'
enough that even two metres above the floor I'd imagine that it would be
relatively motionless and that the gas would evenly distribute itself
throughout the rest of the cylinder.


It would distribute itself with the velocity appropriate to the distance
from the axis, simply because there is nothing to stop it doing so.

Am I right in all this?


Nope. It all boils down to Newton's Law `a body at rest remains at rest and
a body in motion travels at constant speed in a straight line unless acted
upon by a force'. Standing on the floor you are acted upon by a force which
is making you travel in a circle. Once you, or anything else, leaves the
floor you are no longer being acted upon by a force so you travel in a
straight line at the velocity you had the last time you were acted upon by
a force.

Don't listen to anyone who tries to explain it in terms of centrifugal
force. That is a ficitious force that arises when you are moving in a
circle and pretending that you aren't. It's very useful for calculations,
but it obscures the physics and make the explanation harder. The real force
is the one under your feet pushing you into a circle.

Keith Harwood.

 




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