A year-and-half back I went looking up Tsiolkovsky dodges and turned up the space fountain. I took this seriously for Aphrodite Terra if we find our way around the corrosive clouds. Let us talk about Mars, which Weinersmith is taking rather less seriously.
Here's the fun part about Mars - besides that it starts with negligible atmospheric drag and 3.721 m/s2. The shuttle back to interspace just has to hit Deimos. Here's the even funner part: we expect the shuttle, someday, can grab a chain dangling from (5989 km) Phobos. Hollister David for the chain allows 1400-4300 km before it starts dragging the present atmo and (more to the point) groaning under its own mass so let's start at the low end: 4589 km altitude. (UPDATE 2 PM MST - and leaving alone the orbital ring.) Give or take Phobos' eccentricity, which we are also hoping to correct.
MIT's original fountain scheme was for a permanent fixture, for Earthlings to get into (the lowest) orbit. Over Mars, the fountain exists to inject cargo into a 100 km altitude which thence blasts Herr Hohmann to 4589 km.
Downside: a constant tower needs a constant source of energy. Venus has this, in its eternal heavy winds. Earth will have this in geothermal sites, looking especially at such tropics as Indonesia; SpaceX photovoltaics also look good at this timescale. I do not find anywhere in Mars where the energy is renewable, constant, and sufficient. Is there a budget for hoisting a fountain for "only" a century at a time?
How about not building a fountain. Instead: ad-hoc boost a platform to 100 km at 6.1 m/s2, at which altitude said platform fires its rockets. Boost this at night so superconductors give you the magnetism. That's a lot of bullets and casing to clean up afterward; but Rocket Lab can take the casing, and magnetic bullets are literally dirt cheap on Mars. Comparing the energy-budget for all this, with the budget for making hydrogen-heavy explosive chemicals; on Mars, that might be a wash, especially given Mars is low on volatiles.
On Mars, Lofstrom's Launch-Loop or the Bifrost Bridge look better as permanent structures. Once the orbital ring is up, I'd honestly file all these as local solutions: get ores and (maybe especially) water-ice off the more-polar regions, into the equator. Ditto for the Moon given what a joke the pogo turned out to be.
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