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

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In summary, In "Rendezvous with Rama," there is a giant hollow cylinder spaceship that rotates to create artificial gravity. The spaceship also has a cylindrical sea that circumscribes the cylinder, with a height difference between the two shores. A scientist argues that this height difference is to compensate for when the spaceship accelerates, and is able to calculate the maximum acceleration of the spaceship using its rotation speed, mass, and dimensions. The relationship between the vertical heights ratio and the sideways width is equal to the ratio of the central acceleration to the sideways acceleration, and the combined force should be orthogonal to the surface of the cylindrical sea. This insight helps the poster understand the problem better.
  • #1
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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  • #2
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).
 
  • #3
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?
 
  • #4
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.
 
  • #5
Well that was a heck of a lot easier than I was thinking it would be.

Thanks a bunch!
 
  • #6
It wasn't river, it was Cylindrical Sea.
 

1. How is shore height difference solved in "Rendezvous with Rama"?

The shore height difference in "Rendezvous with Rama" is solved using a combination of mathematical calculations, advanced technology, and careful observation. The explorers on the spaceship Endeavour use sonar mapping technology to measure the depth of the water and the height of the shore. They then use trigonometry to calculate the difference in height between the shore and the water's surface.

2. What is the significance of solving the shore height difference in "Rendezvous with Rama"?

The shore height difference is significant in "Rendezvous with Rama" because it provides crucial information about the structure and dimensions of the cylindrical spaceship named Rama. It also helps the explorers determine the exact location of the airlock and the best way to enter and explore the interior of Rama.

3. How accurate is the method used to solve the shore height difference in "Rendezvous with Rama"?

The method used to solve the shore height difference in "Rendezvous with Rama" is highly accurate. The explorers use advanced technology and precise mathematical calculations to measure and calculate the difference in height. However, there is still a margin of error due to the limitations of the technology and the unpredictable nature of the environment.

4. What challenges did the explorers face while solving the shore height difference in "Rendezvous with Rama"?

The explorers faced several challenges while trying to solve the shore height difference in "Rendezvous with Rama." The constantly shifting water levels, unpredictable weather patterns, and the massive size of Rama made it difficult to get accurate measurements. The explorers also had to deal with the pressure and dangers of exploring an unknown alien spacecraft.

5. How does solving the shore height difference contribute to the overall plot of "Rendezvous with Rama"?

Solving the shore height difference is an essential part of the plot of "Rendezvous with Rama." It not only helps the explorers gain access to the interior of Rama but also reveals crucial information about the nature and purpose of the spaceship. It also showcases the ingenuity and resourcefulness of the explorers as they use science and technology to explore and understand the alien world of Rama.

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