Centrifugal force in Rendezvous with Rama

[itchybrain]

SPOILER ALERT: This question will refer to, and may have spoilers, regarding Arthur C Clarke's Rendezvous with Rama. Read below at your own peril.

BTW the book is totally worth reading.

In the book, the astronauts basically encounter an immensely large cylinder, rotating along its long axis at high speeds. Once inside, they describe how along the long axis ("center of the cylinder") there is no sense of gravitational pull, but along the inside shell of the cylinder, a pull is felt.

I believe I understand the concept here. Any force that will "pull" someone "down" (or into the ground) can be compared to a gravitational force. In this particular case, Rama does not distort spacetime and does not create gravitational forces, but the passenger's inertia against the rotation shell simulates gravitation (centrifugal force, though some object to this term).

Now, Rama has an atmosphere. In another part of the book, one of the astronauts "bikes" with a flying bike from one axis to another, and experiences gravitational force of different intensity, depending on the height of the flying trajectory (perpendicular distance from the rotating shell, alternatively the perpendicular distance from the axis). If traveling along the axis, no pull whatsoever is felt.

What is exerting the force on this biking astronaut? Is it Rama's atmosphere? The astronaut, when flying/biking, does not have any contact with the spinning shell.

In other terms, if Rama's atmosphere was evacuated, and one decided to push themselves from one end-axis to the other, would they fell a pull as well if they deviated from the main central axis?

 

[Greg Bernhardt]

Does this discussion shed any light?
http://forums.xkcd.com/viewtopic.php?f=18&t=81975

 

[russ_watters]

I realize you read this in a book, but it is a real physics question, so I'm moving it to "classical physics".

We do also get this question occasionally, but typically referencing climbing a ladder "up" toward the central axis. The answer is the same though, either way (and yes, it is in Greg's link):

First, it is important to understand what the atmosphere is doing. It is rotating with the cylinder and since the cylinder is fairly small, the mass of the air doesn't impact its pressure much (pressure is constant everywhere). So as you go "up", you continue rotating with the atmosphere, but at a decreasing linear speed and therefore against a decreasing "gravitational" force. Traveling along the axis is easy and fun this way, but you must be careful when traveling perpendicular to the axis because your motion will substantially impact the "gravitational" force you feel. Specifically, when you fly along the axis, the lift you require/gravity you feel depends only on your altitude, not your speed. But when you fly perpendicular to the axis, the lift you require/gravity you feel also depends on your speed.

[edit] Oops: I didn't actually answer the question. I described what is felt, but not what causes it. What causes the felt force is the curved path the person must take to maintain his course. It may not look like it to him, but he's actually flying in circles.

The last question is harder and depends on exactly how he achieves the course. If he starts from the side and lifts "up" toward the central axis, he will need a constant force to maintain his altitude because he's still rotating with the cylinder (flying with a circle). But if he starts from the central axis, he's just rotating in place and will not require any forces to maintain linear motion toward the other end of the cylinder once he starts moving.

 

[A.T.]

What is exerting the force on this biking astronaut?

What force exactly, and how is that force measured?

Is it Rama's atmosphere?

If the flying bikes use aerodynamic surfaces, propellers etc. then there will be forces by the air on the bike.

In other terms, if Rama's atmosphere was evacuated, and one decided to push themselves from one end-axis to the other, would they fell a pull as well if they deviated from the main central axis?

No, when in free fall you don’t feel any pull. This is also true for gravity caused by a mass. But your trajectory can still look accelerated from the rotating frame.

Look up "proper acceleration" (feeling a force) vs. "coordinate acceleration" (changing velocity in some frame of reference).

 

[itchybrain]

Thank you, very helpful.

 

[dkotschessaa]

I know this is a two year old thread, but I wanted to thank the contributors. I am reading this book and had the exact same questions.