How many poles and lines would be needed to create a zipline around the world?

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SUMMARY

To create a zipline around the world, multiple poles and lines are necessary due to the curvature of the Earth. A single pole cannot support a continuous line due to the tangent line's properties, which approach infinity. The discussion emphasizes the need for a series of poles positioned at calculated intervals to maintain the zipline's integrity. The exact number of poles and the total length of the lines depend on the chosen angle of descent and the specific calculations of the Earth's circumference.

PREREQUISITES
  • Understanding of basic trigonometry
  • Knowledge of the Earth's circumference (approximately 40,075 kilometers)
  • Familiarity with the concept of tangent lines in geometry
  • Basic physics principles related to forces and tension
NEXT STEPS
  • Calculate the number of poles required based on different angles of descent
  • Research the physics of tension in zipline design
  • Explore mathematical models for approximating curves and tangents
  • Investigate safety regulations and engineering standards for zipline construction
USEFUL FOR

Mathematicians, engineers, adventure park designers, and anyone interested in theoretical applications of physics and geometry in practical scenarios.

steadierfooting
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I was trying to figure this out on my own, probably more a trig question then math though. It''s been a few years since I've taken a physics class so forgive me if I'm misusing terminology.

Let's assume I wanted to create a zipline that would take me around the world. You couldn't jus use a x degree angle and use the circumference of the Earth and have one large pole to reach the sky. I'm guessing there would be multiple exsecent lines (poles) where the next pole would be set up where the tangent line reaches the circle (globe). That tangent line probably approaches infinity so I'm looking for approximations, but.

How many 'zip lines' would there need to be disregarding safety, and how long would the total 'lines' be if we were to create a zipline to go around the world?

Thanks for any advice in helping me solve this problem!
 
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errr hypothetical not theoretical
 

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