Sorry, just returned to correct my error -- I drastically overestimated the velocity gain. In truth you only gain about 2.3 m/s (i.e. 0.03% orbital velocity) when climbing to the top of the elevator. Math is simply final velocity minus initial velocity: https://futureboy.us/fsp/frink.fsp?fromVal=%28earthradius+%2...

>The top of the elevator is travelling at orbital velocity. This is trivial to show in designs with a counterweight.

Per the paper this design only reaches 200 km in altitude, therefore it has no counterweight (a counterweight would need to be somewhere above 35,786 km altitude). Speed at the top is far below orbital velocity, so it requires a method of acceleration.

The paper acknowledges this. From the abstract:

"At the top of the loop, vehicles may be accelerated to orbital velocity or higher by rocket motors, electromagnetic propulsion, or hybrid methods."