The abstract brings up SSTOs, but has there been anything in recent invention that will make them anything other than the white whale people have been chasing since forever?
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SSTO is just marginally possible, if it is possible you need exotic materials and engines and you're never going to get a good payload fraction and adding wings, horizontal takeoff, horizontal landing and such just makes it worse. The one good thing about it is that you get closer to "aircraft-like operations" because in principle you can inspect it, refill it, and relaunch it -- whereas something like the STS or Falcoln 9 or Starship will require stacking up multiple parts for each launch.
My guess is aerospikes are making a comeback though because of interest in hypersonic weapons system. I could also see them being useful for the second stage of something like Starship which mostly operates at high altitudes but has to land at low altitudes. There are a lot of other technical problems, like the thermal management system, which really have to be solved before worrying about that optimization.
Similarly, I assume there are valid reasons SpaceX has chosen not to use aerospike Raptors, especially given their well-earned reputation for innovating things everyone else swore couldn't be done. If even they haven't been able to make it work, that's a strong data point as to the state of the art.
Sure, they talk about Mars, and in-space refueling seems radical, but they've yet to succeed at doing anything radical... yet.
Rumor has it they were struggling with the payload fraction w/ the first generation of Starship and they switched to a second generation that struggles with blowing up. A big advantage of the two-stage architecture is that you can develop the two stages independently. Presumably they will eventually get Starship to orbit and bring it home, they will have plenty of time to improve it get the payload fraction up just as they did with F9.
SpaceX took a lot of ideas which had been individually proven before, and then put in the work to perfect them and integrate them in a production ready spacecraft. That is important work and good engineering, but not radical. An aerospike had literally never been flown to orbit at that time (I think still not), so it would have been a way worse fit for the SpaceX method of developing the Falcon 9.
I think SpaceX didn't try to develop aerospike nozzles because the advantages probably aren't that large compared to the mixed nozzle design they are currently using. They also reused the same ceramic heat shield material developed for the space shuttle instead of developing something new.
Compare that to the cancelled "VentureStar": It would have used both linear aerospike engines and a new metallic thermal protection system (TPS) instead of a ceramic one. I remember an interview where Musk answered the question of why they aren't doing aerospikes or metallic heat shields etc, that there are many ways to skin a cat. They are only doing one thing that they think will work, which is not necessarily the best possible solution, but potentially faster or cheaper to develop.