Solving Shore Height Difference in "Rendezvous with Rama" (Clarke)

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Discussion Overview

The discussion revolves around the height difference between the shores of a river (referred to as a Cylindrical Sea) in Arthur C. Clarke's "Rendezvous with Rama." Participants explore the implications of the rotating cylindrical structure on the water's behavior and the calculations involved in understanding the forces at play, particularly in relation to artificial gravity and acceleration.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the pseudo forces in a non-inertial reference frame and seeks guidance on the general method for solving the problem.
  • Another participant suggests that the tangent of the angle between the surface of the cylinder and the line connecting the two shores should equal the ratio of maximum acceleration to the centripetal force per unit mass.
  • A follow-up inquiry seeks clarification on whether the vertical height ratio to the sideways width corresponds directly to the ratio of central acceleration to sideways acceleration.
  • It is asserted that the combined force should be orthogonal to the surface of the river, implying a relationship between the forces involved.
  • A participant notes that the term "river" is incorrect and clarifies that it should be referred to as a "Cylindrical Sea."

Areas of Agreement / Disagreement

Participants express varying levels of understanding and interpretation of the relationships between the forces involved, with some seeking clarification while others provide insights. No consensus is reached on the overall approach or solution to the problem.

Contextual Notes

Participants mention the need for specific dimensions and calculations, indicating that certain assumptions and details are missing from the discussion. The complexity of fluid mechanics and the treatment of forces in a rotating system are acknowledged but not fully resolved.

Redd
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Hi I'm new here and I figured I would post a question that I have thought about but never really understood from "Rendezvous with Rama" (Clarke)


For those of you who aren't familiar in "Rendezvous with Rama" there is a shapeship that is a giant hollow cylinder.
This cylinder rotates to create artificial gravity. okay.

Now the thing I can't figure out:
Rama also has a river that circumscribes the cylinder.
They discover there is a height difference between the two shores of the river. Later a scientist argues that the difference in shore heights is to compensate for when Rama accelerates (meaning it accelerates in the direction of its circular faces). Then the scientist does a few "quick calculations" and determines how much Rama is capable of accelerating.

They know how fast Rama is rotating, Rama's mass and general dimensions as well as the dimensions of the river. I couldn't find the exact dimensions immediatly but I am curious
more for what general method would be best for this problem.

I think my biggest difficulty is that the "force" that is causing the water to slosh back is a pseudo force that is only a result of the water's non-inertial reference frame, and I frankly have always been rather confused by these ideas. Also I haven't studied anything of even basic fluid mechanics so I'm not sure how to treat the movement of the water. I tried doing some weird calculus stuff to determine the amount of work it would require to lift the amount of water, but It didn't lead to anything recognizably fruitfull.

So any insight? Maybe I misunderstood some aspect of the text (anyone particularly familiar?)
Anyway if you have stuck around this long thanks for any responses :)
 
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The tangent of the angle between the surface of the cylinder and the line connecting two shores should be equal to the ratio of maximum acceleration and the centripetal force per unit mass (r*omega^2).
 
hamster143 said:
The tangent of the angle between the surface of the cylinder and the line connecting two shores should be equal to the ratio of maximum acceleration and the centripetal force per unit mass (r*omega^2).

whoa. That was certainly quick and succinct.

Could you elaborate on this more?

So are you saying the vertical heights ratio to the sideways width is equal to the ratio of the central acceleration to the sideways acceleration?
That seems to make some intuitive sense.
Is it really that direct a relationship?
 
Redd said:
whoa. That was certainly quick and succinct.

Could you elaborate on this more?

So are you saying the vertical heights ratio to the sideways width is equal to the ratio of the central acceleration to the sideways acceleration?
That seems to make some intuitive sense.
Is it really that direct a relationship?

Yes. Because the combined force should be orthogonal to the surface of the river.
 
Well that was a heck of a lot easier than I was thinking it would be.

Thanks a bunch!
 
It wasn't river, it was Cylindrical Sea.
 

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