I have just finished reading this book by Arthur C. Clarke, and while I mostly enjoyed it, there is one thing I cannot wrap my head around.
Near the end of the book, when engineer Morgan uses a Spider to climb up 600km on his tower to bring oxigen and supplies to the people stranded after an accident, the battery goes dead at about 20 meters from his destination.
How did he manage to move those last meters with a totally dead battery?
Valorum's comment is close. The Tower is being built in space and lowered down. It moves down along a "guide tape" which was lowered down from space and attached to the ground earlier. Morgan's vehicle ascended up the same guide tape.
So even though his vehicle is stuck on the tape because it ran out of power, the bottom of the Tower is lowering down towards him as it is being built.
See Chapter 54 "Theory of Relativity".
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